Question

A rectangular loop, of size $10\text{cm}\times 3\text{cm}$, is moving out of a region of uniform magnetic field of $0.5\text{T}$, directed normal inwards into the loop. If we want to move the loop with a constant velocity of $1\text{cm/s}$, the force required is -

Take, resistance of loop $=1\text{m}\Omega$

• A. $2.25\times {10}^{-3}\text{N}$
• B. $4.55\times {10}^{-3}\text{N}$
• C. $9.76\times {10}^{-3}\text{N}$
• D. $1.25\times {10}^{-3}\text{N}$

Answer 1

The correct option is A $2.25\times {10}^{-3}\text{N}$

Emf induced in the loop is,

$E=Bvl=0.5\times {10}^{-2}\times 3\times {10}^{-2}$

$\Rightarrow E=1.5\times {10}^{-4}\text{V}$

Current flowing in the loop is

$i=\frac{E}{R}=\frac{1.5\times {10}^{-4}}{1\times {10}^{-3}}$

$i=0.15\text{A}$

Now, force acting on the loop due to magnetic field,

$F=Bil=0.5\times 0.15\times 3\times {10}^{-2}=2.25\times {10}^{-3}\text{N}$

Therefore, external force required to move the wire with constant velocity is $2.25\times {10}^{-3}\text{N}$.

Hence, option $\left(A\right)$ will be the correct answer.