# A wire of mass 100g is carrying a current of 2A towards increasing x in the form of y = x2 (-2m ≤ x ≤ +2m ) ….

Q. A wire of mass 100g is carrying a current of 2A towards increasing x in the form of y = x2  (-2m ≤  x   ≤ +2m ) . This wire is placed in a magnetic field $\displaystyle \vec{B} = – 0.02 \hat{k}$ The acceleration of the wire (in m/s²) is

(a) $\displaystyle -1.6\hat{j}$

(b) $\displaystyle -3.2\hat{j}$

(c) $\displaystyle 1.6\hat{j}$

(d) zero

Ans: (c)

Sol:

Length of wire from -2 to +2m is

$\displaystyle \vec{L} = 4\hat{i}$

Force acting on the wire is

$\displaystyle \vec{F} = I (\vec{L}\times \vec{B})$

$\displaystyle \vec{F} = 2 (4\hat{i}\times -0.02\hat{k})$

$\displaystyle \vec{F} = 2 (0.08\hat{j}) = 0.16\hat{j}$

Acceleration is

$\displaystyle \vec{a} = \frac{\vec{F}}{m}$

$\displaystyle \vec{a} = \frac{0.16\hat{j}}{100\times 10^{-3}}= 1.6\hat{j}$