In a certain region the magnetic field is uniform in direction but its magnitude…

PHYSICS · Multi-part · CBSE · Physics · Electromagnetic Induction · Electromagnetic Induction

Problem

In a certain region the magnetic field is uniform in direction but its magnitude varies with the

x

-coordinate according to

B(x)=B_{0}(1+kx)

, where

B_{0}=0.20\,\text{T}

and

k=0.10\,\text{m}^{-1}

. A thin conducting rod of length

0.30\,\text{m}

is oriented perpendicular to the field and moves parallel to the

x

-axis with uniform speed

5.0\,\text{m}\,\text{s}^{-1}

. At

t=0

the centre of the rod is at

x=0

. (i) Write an expression for the magnetic field magnitude at the centre of the rod at any time

t

. (ii) Assuming the field is approximately uniform over the length of the rod at each instant, obtain the induced emf as a function of time for

t>0

. (iii) Compute the emf at

t = 2.0\,\text{s}