Question Statement:
The Hamiltonian of a particle is H = P'
- + pq, where q is the generalized coordinate
and p is the corresponding canonical momentum. The Lagrangian is
(A)
m(da + g)
2
(0) 7 (da)
+qda -q
dt
m
(B)
2 di
m
(D)
2
( da
dg
(ất)
-q
-+ q?
dt
A toroidal coil has N closely-wound turns. Assume the current through the coil to be I
and the toroid is filled with a magnetic material of relative permittivity H,. The
magnitude of magnetic induction B inside the toroid, at a radial distance r from the
axis, is given by
(A) H,M,NIr
(B) 4,H.NI
(C) H,H6NI
2r
(D) 2тн,H.NIr
An electromagnetic wave with E(z,f) = E, cos(w t - kz) / is traveling in free space
and crosses a disc of radius 2 m placed perpendicular to the z-axis. If E, = 60 V m''
the average power, in Watt, crossing the disc along the z-direction is
(A) 30
(B) 60
(C) 120
(D) 270
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 the Coulomb gauge.
(C) Yes, provided w = 0.
(B) Yes, in the Lorentz gauge.
(D)
No.
For a particle of mass m in a one-dimensional harmonic oscillator potential of the
form V(x) ==mc'x , the first excited energy eigenstate is 4 (x) = xe*™*
The value
of a is
(A) ma/ 4h
(B) ma/3h
(C) ma/2h
(D) 2ma/3h
If [x,p ]= ih, the value of [x',p] is
(A) 2ihx?
(B) - 2ihx?
(C) 3ihx'
(D) - 3ihx?
PH-8/20
R
Options:
- (A) 2ihx?
- (B) - 2ihx?
- (D) - 3ihx? PH-8/20 R
- (C) 3ihx'