Q. A horizontal straight wire 10 m long extending from east to west is falling with a speed of 5.0 ${ms}^{- 1}$, at right angles to the horizontal component of the earth’s magnetic field of strength $0.30 \times 10^{- 4}{Wbm}^{- 2}.$ the instantaneous value of the induced potential gradient in the wire, from west to east, is
A) $+ 1.5 \times 10^{- 3}\ {Vm}^{- 1}$
B) $- 1.5 \times 10^{- 3}\ {Vm}^{- 1}$
C) $+ 1.5 \times 10^{- 4}\ {Vm}^{- 1}$
D) $- 1.5 \times 10^{- 4}\ {Vm}^{- 1}$
Explanation
(a) Given,$\ B = 0.30 \times 10^{- 4}{Wbm}^{- 2},l = 10\ m$ and $v = 5.0\ {ms}^{- 1}$
The induced potential gradient
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ V = Bvl$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ V = - 0.30 \times 10^{- 4} \times 5 \times 10$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ V = \ - 1.5 \times 10^{- 3}\ {Vm}^{- 1}$
From west to east,
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ V = + 1.5 \times 10^{- 3}{Vm}^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.