Question

A wire carrying a current of 4 A is in a 0.5 T magnetic field as shown above.
If the direction of electron flow is to the right as shown, what is the magnitude and direction of the force (per unit length) on the wire?

• A. $2N/m$ into the page
• B. $8N/m$ out of the page
• C. $2N/m$ to the top of the page
• D. $2N/m$ to the bottom of the page
• E. $8N/m$ to the top of the page

Answer 1

The correct option is D $2N/m$ to the bottom of the page

Given : $\overrightarrow{B}=-0.5$ $\hat{z}$
Current flowing through the wire $\overrightarrow{I}=-4\hat{x}$ A (because current flows in a direction opposite to that of electron flow)

Let the length of the wire be $l$.

Magnetic force $\overrightarrow{F}=I(\overrightarrow{l}\times \overrightarrow{B})=IlB[-\overrightarrow{x}\times (-\hat{z}\left)\right]$

$\therefore$ Force per unit length $\frac{\overrightarrow{F}}{l}=(4\times 0.5)$ $(-\hat{y})=-2$ $\hat{y}$ $N/m$

Hence option D is correct.