165 Official GATE PH Questions with Verified Solutions & Answer Keys
Four point charges are placed in a plane at the following positions: +Q at (1, 0), -Q at (-1, 0), +Q at (0, 1) and -Q at (0, -1). At large distances the electrostatic potential due...
A charged capacitor (C) is connected in series with an inductor (L). When the displacement current reduces to zero, the energy of the LC circuit is (A) stored entirely in its magne...
The wavefunction of a particle, moving in a one-dimensional time-independent potential V(x), is given by y(x) = e~lar+b , where a and b are constants. This means that the potential...
A solid superconductor is placed in an external magnetic field and then cooled below its critical temperature. The superconductor (A) retains its magnetic flux because the surface ...
A particle with energy E is in a time-independent double well potential as shown in the figure. correct? Which of the following statements about the particle is NOT (A) The particl...
The energy levels of a particle of mass m in a potential of the form V(x) = oo, xS0 =mw'x, x>0 are given, in terms of quantum number n = 0,1,2,3,..., by (A) (n+}) ta (B) (2n +}) tr...
The electromagnetic field due to a point charge must be described by Liénard- Weichert potentials when (A) the point charge is highly accelerated. (B) the electric and magnetic fie...
Match the following P. rest mass 1. timelike vector Q. charge 2. Lorentz invariant R. four-momentum 3. tensor of rank 2 S. electromagnetic field 4. conserved and Lorentz invariant ...
Can the following scalar and vector potentials describe an electromagnetic field? Ф(7,t) = 3xyz - 4t Ä(F,1) = (2x- at)Î + (y- 22) ] + (2-2xe'*)k where w is a constant. (A) Yes, in ...
There are only three bound states for a particle of mass m in a one-dimensional -a/2 +a/2 potential well of the form shown in the \cdot x figure. The depth Vo of the potential sati...
A piece of paraffin is placed in a uniform magnetic field Ho. The sample contains hydrogen nuclei of mass mp. which interact only with external magnetic field. An additional oscill...
The solid phase of an element follows van der Waals bonding with inter-atomic potential V(r) = -- ,o+ ,iz, where P and Q are constants. The bond length can be expressed as (A) (22)...
A parallel plate capacitor is being discharged. What is the direction of the energy flow in terms of the Poynting vector in the space between the plates? 3 >ý (A) Along the wire in...
Unpolarized light falls from air to a planar air-glass interface (refractive index of glass is 1.5) and the reflected light is observed to be plane polarized. The polarization vect...
Under normal operating conditions, the gate terminal of an n-channel junction field effect transistor (JFET) and an n-channel metal oxide semiconductor field effect transistor (MOS...
A dielectric sphere is placed in a uniform electric field directed along the positive y-axis. Which one of the following represents the correct equipotential surfaces? (A) (B) x (C...
A rod of length L with uniform charge density & per unit length is in the xy-plane and rotating about z-axis passing through one of its edge with an angular velocity c as shown in ...
Corcos0 -. The A circular disc of radius a on the xy plane has a surface charge density o = a electric dipole moment of this charge distribution is о ла" oora' (D) -- Cora* 4 (С) -...
A system containing N non-interacting localized particles of spin ½ and magnetic moment u each is kept in constant external magnetic field B and in thermal equilibrium at temperatu...
An electrostatic field È exists in a given region R. Choose the WRONG statement. (A) Circulation of E is zero (B) E can always be expressed as the gradient of a scalar field (C) Th...
A conducting loop L of surface area S is moving with a velocity in a magnetic field B(F,t) = B,?, B, is a positive constant of suitable dimensions. The emf induced, Vemf , in the l...
A superconducting ring is cooled in the presence of a magnetic field below its critical temperature (Tc). The total magnetic flux that passes through the ring is (A) zero (B) 2e C)...
The magnetic field (in A m') inside a long solid cylindrical conductor of radius a = 0.1 m is, H = 10* , sin(ar) - [ cos(ar) ₫, where a =- \cdot. What is the total current (in A) i...
Which one of the following current densities, J, can generate the magnetic vector potential Ä=(v{+x']) ? (A) 2 (xỉ + xộ) (B) - 2 (i+j) (C) - 2 (i-3) (D) 2(xỉ -xộ) e*...
In a non-conducting medium characterized by & = 6., M= M. and conductivity o = 0, the electric field (in V m') is given by Ë = 20sin [10%/ - kz ]}. The magnetic field, F (in A m'),...
A cylindrical rod of length L and radius r, made of an inhomogeneous dielectric, is placed with its axis along the z direction with one end at the origin as shown below. If the rod...
The probability that an energy level e at a temperature T is unoccupied by a fermion of chemical potential y is given by (A) đe-A) aT +T (B) TO-A NAT -T CO eMONtOT +T ) a-oa -...
In an experiment involving a ferromagnetic medium, the following observations were made. Which one of the plots does NOT correctly represent the property of the medium? (T_c is the...
Two states of an atom have definite parities. An electric dipole transition between these states is (A) Allowed if both the states have even parily (B) Allowed if both the states h...
Two states of an atom have definite parities. An electric dipole transition beiween these states is (A) Allowed if both the states have even parily (B) Allowed if both the states h...
An insulating sphere of radius a carries a charge density p(F) = po(a'-r*) cos0; r<a. The leading order term for the electric field al a distance d, far away from the charge distri...
Far away from any of the resonance frequencies of a medium, the real part of the dielectric permittivity is (A) Always independent of frequency (C) Monotonically increasing with (B...
Far away fromn any of the resonance frequencies of a medium, the real part of the dielectric permittivity is (A) Always independent of frequency (B) Monotonically decreasing with f...
Match the typical spectra of stable molecules with the corresponding wave-number range 1. Electronic spectra i. 10° cm' and above 2. Rotational spectra ii. 10% -10° cm' 3. Molecula...
Consider the operations P. 7 → (parity) (parity) and T: ->- (time-reversal. For the electric and magnetic fields E and B, which of the following set of transformations is correct? ...
Consider a conducting joop of radius a and total loop resistance R placed in a region with a magnetic field & thereby enclosing a flux d. The luop is connecied to an electronic cir...
For a spin-s particle, in the eigen basis of 5%. S, the expoctation value (sm|S; (sm) is (A) - Nfs(s+1)-m'} (B) s°(s(s+1)-2m*) 2 (C) 1°{s(s+1)-mi*} (D) n'm PH 11/24 2010 0.45 A par...
The spectral line cortesponding to the transition =Px (m,=+2) →'Sy(m,==}) is observed along the direction of the applied magnetic field. The emitted electromagnetic fieid is (A) Ci...
For a plane wave of angular frequency « and propagation vector i propagating in the medium Maxwell's equations reduce to (A) k -Ë =0; *\cdotR =0; kxÊ=шеЙ; k×R=-шuË (в) к-Ё=0; К.F=0...
An electron with energy E is incident from left on a potential barrier, given by V(x) =0 forx<0 =V forx> 0 as shown in the figure. V(x) --->E 0 For E < Vo, the space part of the wa...
Two charges q and 2q are placed along the x-axis in front of a grounded, infinite conducting plane, as shown in the figure. They are located respectively at a distance of 0.5 m and...
Which of the following expressions for a vector potential Ä DOES NOT represent a uniform magnetic field of magnitude B, along the z-direction? (A) Ä =(0,B,x,O) (B) А =(-B,y,0,0) (C...
A particle is moving under the action of a generalized potential V(q,9) = (I+4) The magnitude of the generalized force is (A) . 2(1+q) (в) 2(1-4) (C) 9 (D)...
A spherical conductor of radius a is placed in a uniform electric field E = E,k . The potential at a point P(r,0) for r > a, is given by p(r,0) = constant- E,rcos0+- E,a' p?COSO wh...
For the value of a determined in Q. 52, the expectation value of energy of the oscillator in the state W, is (A) h0 (B) 3hw/2 (C) 3h0 (D) 9h0/2 Statement for Linked Answer Question...
The electric field Ë(x, y, z,t) corresponding to the above wave is given by (A) cB, sin (x+y) k + wt (-]) V2 (B) CB sin (x+») z + ar |"13) (C) cB, sin/ (x+y)- K+ ur i D) cB, sin (x...
The average Poynting vector is given by (A) ,CB? (Î- ]) (B) _CBẻ (Î -]) 2M. 2M. V2 (C) CBẻ (+ i) 52 (D)_CB: (Î +]) 2M0 V2 PH 12/20 2011 PH General Aptitude (GA) Questions...
The electric and the magnetic fields ( , ) E z t and ( , ) B z t , respectively corresponding to the scalar potential (z,t) = 0 and vector potential ( , ) A z t itz are...
A particle of unit mass moves along the x-axis under the influence of a potential, 2 ( ) 2 V x x x - . The particle is found to be in stable equilibrium at the point 2 x . T...
A particle is constrained to move in a truncated harmonic potential well (x > 0) as shown in the figure. Which one of the following statements is CORRECT?...
A plane polarized electromagnetic wave in free space at time 0 t is given by ( , ) 10 exp[ (6 8 )] E x z j i x z . The magnetic field ( , , ) B x z t is given by...
Two infinitely extended homogeneous isotropic dielectric media (medium-1 and medium-2 with dielectric constants 1 0 2 and 2 0 5 , respectively) meet at the z = 0 plane as...
A paramagnetic system consisting of N spin-half particles, is placed in an external magnetic field. It is found that N/2 spins are aligned parallel and the remaining N/2 spins are ...
The probability current density for the real part of the wavefunction is (A) 1 (B) k m (C) 2 k m (D) 0 Common Data for Questions 50 and 51: The dispersion relation for a one dimens...
The force constant between the nearest neighbour of the lattice is (M is the mass of the atom) (A) 2 4 MA (B) 2 2 MA (C) 2 MA (D) 2 2 MA 2012 PHYSICS - PH PH 13/20 Linked Answer Qu...
Consider the scattering of neutrons by protons at very low energy due to a nuclear potential of range r0. Given that, ߛ k where δ is the phase shift, k the wave number and ) the lo...
At a surface current, which one of the magnetostatic boundary condition is NOT CORRECT?...
Consider a gas of atoms obeying Maxwell-Boltzmann statistics. The average value of in \vecԦ . Ԧ over all the momenta Ԧ of each of the particles (where aԦ is a constant vector and ...
A charge distribution has the charge density given by _0)} . For this charge distribution the electric field at _0,0 , 0) (A) 2ො \pi\varepsilon_00^2 (B) ො 4\pi\varepsilon_00 (C) ො ...
A monochromatic plane wave at oblique incidence undergoes reflection at a dielectric interface. If in , and ො are the unit vectors in the directions of incident wave, reflected ...
In a normal Zeeman effect experiment, spectral splitting of the line at the wavelength 643.8 nm corresponding to the transition 2 1 1 of cadmium atoms is to be observed. The spectr...
Which one of the following quantities is invariant under Lorentz transformation? (A) Charge density (B) Charge (C) Current (D) Electric field...
The electric field of a uniform plane wave propagating in a dielectric, non-conducting medium is given by, ( )z txE ππ 4 . 0 10 6cos10ˆ 7 − ×= V/m. The phase velocity of the wave...
The ground state and the first excited state wave functions of a one dimensional infinite potential well are ψ1 and ψ2, respectively. When two spin-up electrons are placed in this ...
If the vector potential ,ˆ3ˆ2ˆ z z y y x x A− + =α satisfies the Coulomb gauge, the value of the constant α is ___________________ ....
A particle of mass m is in a potential given by ,3) ( 3 2 0 r ar r ar V + − = where a and r0 are positive constants. When disturbed slightly from its stable equilibrium position, i...
A particle of mass 𝑚𝑚 is subjected to a potential, 𝑚𝑚(𝑥𝑥, 𝑦𝑦) = 1 2 𝑚𝑚\omega\omega2(𝑥𝑥2 + 𝑦𝑦2), −∞ ≤ 𝑥𝑥 ≤ ∞, −∞ ≤ 𝑦𝑦 ≤ ∞ The state with energy 4\hbar\omega\omega ...
A ray of light inside Region 1 in the xy- plane is incident at the semicircular boundary that carries no free charges. The electric field at the point ( )0 , /4P r π in plane polar...
A particle is confined to a one dimensional potential box with the potential ( ) otherwise, 0 , 0 ∞ = < < =a xx V If the particle is subjected to a perturbation, within the box, x ...
A low pass filter is formed by a resistance R and a capacitance C. At the cut-off angular frequency 1 c RCω = , t he voltage gain and the phase of the output voltage relative to th...
R (D) Ф In Bose-Einstein condensates, the particles (A) have strong interparticle attraction (B) condense in real space (C) have overlapping wavefuntions (D) have large and positiv...
Consider a system of N non-interacting spin-½ particles, each having a magnetic moment p, is in a magnetic field B = B ?. If E is the total energy of the system, the number of acce...
For a black body radiation in a cavity, photons are created and annihilated freely as a result of emission and absorption by the walls of the cavity. This is because (A) the chemic...
A point charge is placed between two semi-infinite conducting plates which are inclined at an angle of 30° with respect to each other. The number of image charges is...
The space between two plates of a capacitor carrying charges +Q and -Q is filled with two different dielectric materials, as shown in the figure. Across the interface of the two di...
The binding energy per molecule of NaCl (lattice parameter is 0.563 nm) is 7.95 eV. The repulsive term of the potential is of the form yo, where K is a constant. The value of the M...
The number of permitted transitions from ?P3/2 → 3S12 in the presence of a weak magnetic field is...
A charge -q 15 distributed unformly over a sphere, with a positive charge q at its center in (1) Also in (11), a charge -q is distributed uniformly over an ellipsod with a positive...
Question Type : MCO In the nuclear shell model, the potential is modeled as 1(r) == mor'-AL-S, 2>0. The correct spin - parity and isospin assignments for the ground state of 3C' is...
A particle is confined in a box of length L as shown below. Vo 1 L/2 If the potential Vo is treated as a perturbation, including the first order correction, the ground state energy...
The entropy of a gas containing N particles enclosed in a volume V is given by aVE/ S = Nkg In (w% Where is the total energy, a is a constant and kg is the Boltzmann constant. The ...
Which of the following magnetic vector potentials gives rise to a uniform magnetic field $B_0\hat{k}$?...
The scattering of particles by a potential can be analyzed by Born approximation. In particular, if the scattered wave is replaced by an appropriate plane wave, the corresponding B...
A hydrogen atom is in its ground state. In the presence of a uniform electric field E = E,Ê, the leading order change in its energy is proportional to (E,)". The value of the expon...
An infinite, conducting slab kept in a horizontal plane carries a uniform charge density o. Another infinite slab of thickness t, made of a linear dielectric material of dielectric...
An alpha particle is accelerated in a cyclotron. It leaves the cyclotron with a kinetic energy of 16 MeV. The potential difference between the D electrodes is 50 kilovolts. The num...
The electric field component of a plane electromagnetic wave travelling in vacuum is given by E(z,t) = E, cos(kz -@t)f. The Poynting vector for the wave is (A) (c8,/2) E} cos'(kz-w...
If x and p are the x components of the position and the momentum operators of a particle respectively, the commutator [x2 ',p'] is (A) ih(xp - px) (C) ih(xp + px) (B) 2ih(xp - px) ...
The x-y plane is the boundary between free space and a magnetic material with relative permeability \mu_r. The magnetic field in the free space is B_x \hat{i} + B_z \hat{k}. The ma...
A particle of mass m and energy E, moving in the positive x direction, is incident on a step potential at x = 0, as indicated in the figure. The height of the potential is Vo, wher...
Identical charges q are placed at five vertices of a regular hexagon of side a. The magnitude of the electric field and the electrostatic potential at the centre of the hexagon are...
A parallel plate capacitor with square plates of side 1 m separated by 1 micro meter is filled with a medium of dielectric constant of 10. If the charges on the two plates are 1 C ...
A monochromatic plane wave in free space with electric field amplitude of 1 V/m is normally incident on a fully reflecting mirror. The pressure exerted on the mirror is _x10-12 Pa....
Three charges (2 C, -1 C, -1 C) are placed at the vertices of an equilateral triangle of side 1m as shown in the figure. The component of the electric dipole moment about the marke...
An infinite solenoid carries a time varying current I(t) = At* with A # 0. The axis of the solenoid is along the 2 direction. 7 and are the usual radial and polar directions in cyl...
A free electron of energy 1 eV is incident upon a one-dimensional finite potential step of height 0.75 eV. The probability of its reflection from the barrier is _ (up to two decima...
Consider a one-dimensional potential well of width 3 mm. Using the uncertainty principle (Ar:Ap=½) an estimate of the minimum depth of the well such that it has at least one bound ...
In the context of small oscillations, which one of the following does NOT apply to the normal coordinates? (A) Each normal coordinate has an eigen-frequency associated with it (B) ...
The number of independent components of a general electromagnetic field tensor is...
A particle moves in one dimension under a potential V (x) = a|x| with some non-zero total energy. Which one of the following best describes the particle trajectory in the phase spa...
Consider an infinitely long solenoid with N turns per unit length, radius R and carrying a current I(t) = a cos wt, where a is a constant and w is the angular frequency. The magnit...
A constant and uniform magnetic field B = Bok pervades all space. Which one of the following is the correct choice for the vector potential in Coulomb gauge? (A) -Bo(x+y)î (B) Bo(x...
A long straight wire, having radius a and resistance per unit length r, carries a current 1. The magnitude and direction of the Poynting vector on the surface of the wire is (A) 12...
A p-doped semiconductor slab carries a current / = 100 mA in a magnetic field B = 0.2 T as shown. One measures Vy = 0.25 mV and V, = 2 mV. The mobility of holes in the semiconducto...
An a particle is emitted by a 290Th nucleus. Assuming the potential to be purely Coulombic beyond the point of separation, the height of the Coulomb barrier is MeV (up to two decim...
The ground state energy of a particle of mass m in an infinite potential well is Eo. It changes to Eo(1 + a X 10-3), when there is a small potential bump of height Vo = T2 n2 50mLz...
An electromagnetic plane wave is propagating with an intensity I = 1.0 x 105 Wm 2 in a medium with € = 3€o and M = Mo. The amplitude of the electric field inside the medium is x 10...
An atom in its singlet state is subjected to a magnetic field. The Zeeman splitting of its 650 nm spectral line is 0.03 nm. The magnitude of the field is Tesla (up to two decimal p...
An electric field $\vec{E} = E_0\hat{z}$ is applied to a Hydrogen atom in $n = 2$ excited state. Ignoring spin, the $n = 2$ state is fourfold degenerate, which in the $(l, m)$ basi...
The electric field of an electromagnetic wave is given by ( ) ˆ 3sin E kz t x ω = − + ( ) ˆ 4cos kz t y ω − . The wave is (a) Linearly polarized at an angle 1 4 tan 3 − ...
An infinitely long thin cylindrical shell has its axis coinciding with the z -axis. It carries a surface charge density 0 cos σ φ , where φ is the polar angle and 0 σ is a constant...
A circular loop made of a thin wire has radius 2cm and resistance2Ω. It is placed perpendicular to a uniform magnetic field of magnitude 0 0.01 B = Tesla. At time 0 t = the field...
The electric field of an electromagnetic wave in vacuum is given by ( ) 9 0 ˆ cos 3 4 1.5 10 E E y z t x = + − × The wave is reflected from the 0 z = surface. If the pressure exe...
A conventional type-I superconductor has a critical temperature of 4.7 K at zero magnetic field and a critical magnetic field of 0.3 Tesla at 0 K . The critical field in Tesla at 2...
A particle of mass m moves in a lattice along the x - axis in a periodic potential ( ) ( ) V x V x d = + with periodicity d . The corresponding Brillouin zone extends from 0k − to ...
In a set of N successive polarizers, the th m polarizer makes an angle 2 m N π with the vertical. A vertically polarized light beam of intensity 0I is incident on two s...
A ball bouncing of a rigid floor is described by the potential energy function ( ) for 0 for 0 mgx x V x x > = ∞ ≤ Which of the following schematic diagrams best represents th...
An infinitely long wire parallel to the x -axis is kept at z d = and carries a current I in the positive x direction above a superconductor filling the region 0 z ≤ (see figure). T...
The vector potential inside a long solenoid with n turns per unit length and carrying current I , written in cylindrical coordinates is ( ) 0 ˆ , , 2 nI A s z s µ φ φ = . If the ...
Consider a system of three charges as shown in the figure below: For 10 ; 60 r m θ = = degrees; 6 10 q − = Coulomb, and 3 10 d m − = , the electric dipole potential in volts (round...
A quantum particle is subjected to the potential 00, x5-2 00, x2% The ground state wave function of the particle is proportional to (A) (B) (C) (D) sin( *) cos za) cos...
A particle X is produced in the process it + p→K*+ X via the strong interaction. If the quark content of the K* is us, the quark content of X is cs und uuS ud A medium (Er > 1, M, ...
Choose the correct statement related to the Fermi energy (Ep) and the chemical potential (M) of a metal. (A) (B) (C) (D) # = Ep only at 0 K M = Ep at finite temperature M< EpatoK M...
Which one of the following relations determines the manner in which the electric field lines are refracted across the interface between two dielectric media having dielectric const...
A conducting sphere of radius 1 m is placed in air. The maximum number of electrons that can be put on the sphere to avoid electrical breakdown is about 7x10", where n is an intege...
A uniform magnetic field B = Boy exists in an inertial frame K. A perfect conducting sphere moves with a constant velocity V = Yo with respect to this inertial frame. The rest fram...
The potential energy of a particle of mass m is given by U(x) = asin(k}x - 7/2), a>0, k° >0. The angular frequency of small oscillations of the particle about x = 0 is (A) k2. 2a m...
The radial wave function of a particle in a central potential is given by R(r) = 1" exp Za , where A is the normalization constant and a is positive constant of suitable dimensions...
A free particle of mass M is located in a three-dimensional cubic potential well with impenetrable walls. The degeneracy of the fifth excited state of the particle is...
0+,2*, 4+ -23/2+ 1200 1000 800 600 400 200 -19/2+ 0+ -15/2* 11/2+ 7/2+ Set I Set II For the given sets of energy levels of nuclei X and Y whose mass numbers are odd and even, respe...
Consider a system of three distinguishable particles, each having spin S = 1/2 such that Sz = 1/2 with corresponding magnetic moments Mz = tu. When the system is placed in an exter...
On the surface of a spherical shell enclosing a charge free region, the electrostatic potential values are as follows: One quarter of the area has potential 𝜙_0, another quarter h...
A point charge q is performing simple harmonic oscillations of amplitude A at angular frequency \omega. Using Larmor's formula, the power radiated by the charge is proportional to...
Electric field is measured along the axis of a uniformly charged disc of radius 25 cm. At a distance d from the centre, the field differs by 10% from that of an infinite plane havi...
Consider a non-interacting gas of spin 1 particles, each with magnetic moment 𝜇, placed in a weak magnetic field B, such that L ≪ 1. The average magnetic moment of a particle is...
A parallel plate capacitor with spacing $d$ and area of cross-section $A$ is connected to a source of voltage $V$. If the plates are pulled apart quasistatically to a spacing of $2...
A junction is formed between a metal on the left and an n-type semiconductor on the right. Before forming the junction, the Fermi level EF of the metal lies below that of the semic...
A current of 1 A is flowing through a very long solenoid made of winding density 3000 turns/m. As shown in the figure, a parallel plate capacitor, with plates oriented parallel to ...
The figure schematically shows the M (magnetization) - H (magnetic field) plots for certain types of materials. Here M and H are plotted in the same scale and units. Which one of t...
Consider an isolated magnetized sphere of radius R with a uniform magnetization M⃗⃗ along the positive z direction, with the north and south poles of the sphere lying on the z axis...
A particle of mass m is free to move on a frictionless horizontal two dimensional (r, 𝜃) plane, and is acted upon by a force F = - k 2r3 r̂ with k being a positive constant. If pr...
Consider two real functions U(x, y) = xy(x2 - y2) , V(x, y) = ax4 + by4 + cx2y2 + k , where k is a real constant and a, b, c are real coefficients. If U(x, y) + i V(x, y) is analyt...
Young's double slit experiment is performed using a beam of C60 (fullerene) molecules, each molecule being made up of 60 carbon atoms. When the slit separation is 50 nm, fringes ar...
Under parity and time reversal transformations, which of the following statements is(are) TRUE about the electric dipole moment p and the magnetic dipole moment 𝝁 ?...
Two independent electrostatic configurations are shown in the figure. Configuration (I) consists of an isolated point charge q = 1 C, and configuration (II) consists of another ide...
An infinitely long cylinder of radius R carries a frozen -in magnetization M⃗⃗ = ke-sẑ, where k is a constant and s is the distance from the axis of cylinder. The magnetic permeab...
Let P, Q and R be three different nuclei. Which one of the following nuclear processes is possible?...
In a parallel plate capacitor, the plate at x = 0 is grounded and the plate at x = d is maintained at a potential V0. The space between the two plates is filled with a linear diele...
Consider two matrices: P = [1 2 0 1] and Q = [1 0 0 1]. Which of the following statement is/are true?...
Two point charges of charge +q each are placed a distance 2d apart. A grounded solid conducting sphere of radius a is placed midway between them. Assume a2 ≪ d2. Which of the follo...
As per the Drude model of metals, the electrical resistance of a metallic wire of length L and cross-section area A is (Consider 𝜏 as the relaxation time , m as electron mass, n a...
A paramagnetic material containing paramagnetic ions with total angular momentum J = 1 2 is kept at absolute temperature T. The ratio of the magnetic field required for 80% of the ...
Potential energy of two diatomic molecules P and Q of the same reduced mass is shown in the figure. According to this diagram, which of the following option (s) is/are correct?...
A linear dielectric sphere of radius R has a uniform frozen-in polarization along the z-axis. The center of the sphere initially coincides with the origin, about which the electric...
The screened nuclear charge of neutral Helium atom is given as 1.7e, where e is the magnitude of the electronic charge. Assuming the Bohr model of the atom for which the energy lev...
A thin circular ring of radius R lies in the xy plane with its centre coinciding with the origin. The ring carries a uniform line charge density 𝜆. The quadrupole contribution to ...
A point charge q is placed at a distance d above an infinite, grou nded conducting plate placed on the xy plane at z = 0. The electrostatic potential in z > 0 region is given by \p...
A neutral conducting sphere of radius R is placed in a uniform electric field of magnitude E0, that points along the z axis. The electrostatic potential at any point r outside the ...
A point charge q is placed at the origin, inside a linear dielectric medium of infinite extent, having relative permittivity \epsilonr. Which o f the following option (s) is/are co...
Cyclotrons are used to accelerate ions like deuterons (d) and \alpha particles. Keeping the magnetic field same for both, d and \alpha are extracted with energies 10 MeV and 20 MeV...
Which of the following options is correct for transformation of electric field E⃗ and magnetic field B⃗ under time reversal, i.e., t → -t ?...
On a horizontal plane, a projectile of mass m is launched from the ground with speed v0 at an angle 𝜃0 with the horizontal. In addition to the gravitational force (mg), it also ex...
A dielectric sphere carries a uniform polarization P = 26 μC. cm-2. The magnitude of the electric field at the center of the sphere is E × 109 N. C-1 . The value of E (rounded off ...
In the circuit shown, V(t) = 2 sin(2000𝜋t) Volts, where t is in seconds, which of the following options is correct? (take the opamp to be ideal)...
Considering the circuit and the associated signals measured at different pins (numbered as 1, 2, 3, 4, 5) shown in the figure, the correct option is...