Question

A current of 1 A is flowing along positive x-axis through a straight wire of length 0.5 m placed in a region of a magnetic field given by $\overrightarrow{B}=(2\hat{i}+4\hat{j})$ T. The magnitude and the direction of the force experienced by the wire respectively are:

• A. $\sqrt{18}N$, along positive z-axis
• B. $\sqrt{20}N$, along positive x-axis
• C. $2N$, along positive z-axis
• D. $4N$, along positive y-axis

Answer 1

The correct option is C $2N$, along positive z-axis

Current flowing in the wire $\overrightarrow{I}=1\hat{i}$ A

Length of the wire $l=0.5$ m

Magnetic field $\overrightarrow{B}=(2\hat{i}+4\hat{j})$ T

Force experienced by the wire $\overrightarrow{F}=I(\overrightarrow{l}\times \overrightarrow{B})$

$\therefore$ $\overrightarrow{F}=\left(0.5\right)[1\hat{i}\times (2\hat{i}+4\hat{j}\left)\right]=\left(0.5\right)(1\hat{i}\times 4\hat{j})$

$⟹$ $\overrightarrow{F}=\left(0.5\right)\left(4\right)\hat{k}=2\hat{k}$ N

Hence option C is correct.