Q. A wire of mass 100g is carrying a current of 2A towards increasing x in the form of y = x^{2} (-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} $