CSIR Physical Sciences: Questions 167 - 169 of 389

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Question number: 167

» Electromagnetic Theory » Laplace and Poisson Equations

Appeared in Year: 2011

MCQ▾

Question

The electrostatic potential V(x,y) in free space in a region where the charge density ρ is zero is given by V(x,y)=4e2x+f(x)3y2 . Given that the x – component of the electric field, Ex and V are zero at the origin, f(x) is – (June)

Choices

Choice (4) Response

a.

4e2x8

b.

3x24e2x

c.

3x24e2x+16x

d.

3x24e2x+8x

Question number: 168

» Mathematical Methods of Physics » Elements of Complex Analysis

Appeared in Year: 2014

MCQ▾

Question

Consider the function f(z)=1zln(1z) of a complex variable z=reiθ(r0,<θ<) . The singularities of f(z) are as follows: (December)

Choices

Choice (4) Response

a.

branch points at z=1 and z= ; and a pole at z=0 for all θ .

b.

branch points at z=0,z=1 and z=

c.

branch points at z=1 and z= ; and a pole at z=0 for all θ other than 0θ<2π

d.

branch points at z=1 and z= ; and a pole at z=0 only for 0θ<2π .

Question number: 169

» Quantum Mechanics » Eigenvalue Problems

Appeared in Year: 2014

MCQ▾

Question

The Hamiltonian H0 for a three – state quantum system is given by matrix, H0=(100020002) . When perturbed by H=ε(010101010); where ε1 , the resulting shift in the energy eigenvalue E0=2 is (December)

Choices

Choice (4) Response

a.

ε.2ε

b.

±ε

c.

±2ε

d.

ε,2ε

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