Electromagnetic Theory (CSIR Physical Sciences): Questions 53 - 54 of 57

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Question number: 53

» Electromagnetic Theory » Electromagnetic Induction

Appeared in Year: 2011

MCQ▾

Question

Consider a solenoid of radius R with n turns per unit length, in which a time dependent current I=I0sinωt (where ωRc1 ) flows. The magnitude of the electric field at a perpendicular distance r<R from the axis of symmetry of the solenoid, is – (December)

Choices

Choice (4) Response

a.

0

b.

12rωμ0nI0R2cosωt

c.

12ωμ0nI0rsinωt

d.

12ωμ0nI0rcosωt

Question number: 54

» Electromagnetic Theory » Scalar and Vector Potentials

Appeared in Year: 2011

MCQ▾

Question

The Lagrangian of a particle of charge e and mass m in applied electric and magnetic field is given by L=12mv2+eAveϕ , where A and ϕ are the vector and scalar potentials corresponding to the magnetic and electric fields, respectively. Which of the following statement is correct? (June)

Choices

Choice (4) Response

a.

Under a gauge transformation of the potentials, L changes by the total time derivative of a function of r and t .

b.

The canonically conjugate momentum of the particle is given by p=mv

c.

L remains unchanged under a gauge transformation of the potentials

d.

The Hamiltonian of the particle is given by H=p22m+emAp+eϕ

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