Question

A wire of mass 100 g is carrying a current of 2A towards increasing x in the form of $y=x^2(-2m\le x\le +2m)$.This wire is placed in a magnetic field $\overrightarrow{B}=-0.02\hat{k}$ tesla.The acceleration of the wire (in $m/s^2$) is

• A. $-1.6\hat{j}$
• B. $-3.2\hat{j}$
• C. $1.6\hat{j}$
• D. zero

Answer 1

The correct option is C $1.6\hat{j}$

Force on a current carrying conductor is given by $\overrightarrow{F}=i\overrightarrow{l}\times \overrightarrow{B}$ , The parabolic wire can be replaces with a straight wire extending from -2 to +2 as net force on a closed loop is zero a straight wire with current in same direction of x axis can be assumed in place of parabolic wire.

$\overrightarrow{F}=2\times 4\hat{i}\times -0.02\hat{k}$

$\overrightarrow{F}=8\hat{i}\times -0.02\hat{k}=.16\hat{j}$

acceleration $a=\overrightarrow{F}m=\frac{.16}{10\times {10}^{-3}}=1.6$ N.