Question

A current carrying conductor PQ of length 1m,mass 4.4 x ${10}^{-3}$kg and resistance 50 mili-ohm is kept in a uniform magnetic field of 1.8m T as shown.
a)Indicate the direction of the force on PQ.
b)Calculate the potential v that must be applied to the conductor PQ so that it remains in equilibrium in the magnetic field.

Answer 1

The force is given by-

$\left(a\right)$ $\overrightarrow{F}=l\overrightarrow{i}\times \overrightarrow{B}$

Hence, direction of force on PQ is upward.

$\left(b\right)$ For equilibrium-

Magetic force$=ilB=mg=$ weight

$⟹\frac{V}{R}lB=mg$

$⟹V=\frac{Rmg}{lB}$

$⟹V=\frac{50\times {10}^{-3}\times 44\times {10}^{-3}\times 9.8}{1\times 1.8\times {10}^{-3}}$

$⟹V=12V$