Physics

Problem

A straight metal rod of length

0.40\,\text{m}

rests on horizontal, friction-free rails. A uniform magnetic field of magnitude

0.50\,\text{T}

is directed vertically upward in the entire region. Beginning at

t=0

, the rod is pulled along the rails so that its speed varies with time according to

v = 3t\,\text{m}\,\text{s}^{-1}

(where

t

is in seconds). Answer the following: a. (i) State the relation connecting the magnitude of the induced emf

\mathcal{E}

in the rod with the magnetic field

B

, the length

\ell

of the rod and its speed

v

. b. (ii) Using the given speed–time law, obtain an expression for

\mathcal{E}(t)

. c. (iii) Calculate the magnitude of the emf at

t = 2.0\,\text{s}

. d. (iv) Which end of the rod (front or back) will be at the higher potential at this instant? Give a reason based on Lenz’s law.