Question

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. $-1.5 \times 10^{-4} \,Vm ^{-1}$

Answer 1

Answer: (C)

Given, $B=0.30 \times 10^{-4} \,Wb \,m ^{-2}, v=5\, ms ^{-1}$ and $l=10 \,m$

As induced emf or potential, $e=B v l$
So, induced potential gradient $=\frac{e}{l}=B v$
$=0.3 \times 10^{-4} \times 5=1.5 \times 10^{-4} \,Vm ^{-1}$
Here, East end $B$ at positive potential gradient means increasing potential.