Question

A charge $+2q$ moves vertically upwards with speed $v$, a second charge $-q$ moves horizontally to the right with the same speed $v$, and a third charge $+q$ moves horizontally to the right with the same speed $v$. The point $P$ is located a perpendicular distance $a$ away from each charge as shown in the figure. The magnetic field at point $P$ is

• A. Into the page with magnitude $\frac{{\mu }_0}{4\pi }\frac{2qv}{a^2}$
• B. Into the page with magnitude $\frac{{\mu }_0}{4\pi }\frac{4qv}{a^2}$
• C. Out of the page with magnitude $\frac{{\mu }_0}{4\pi }\frac{2qv}{a^2}$
• D. Out of the page with magnitude $\frac{{\mu }_0}{4\pi }\frac{4qv}{a^2}$

Answer 1

The correct option is D Out of the page with magnitude $\frac{{\mu }_0}{4\pi }\frac{4qv}{a^2}$

Here are, 4 charges as follows

-q at 'a' distance with 'V' velocity.

+2q at 'a' distance with 'V' velocity.

+q at 'a' distance with 'V' velocity, from P

Thus $(\text{magnetic filed}{)}_{net}\text{at}P={\left[{\left(\overrightarrow{B}\right)}_{net}\right]}_P=?$

${\left({\overrightarrow{B}}_{net}\right)}_P={\overrightarrow{B}}_{-q}+{\overrightarrow{B}}_{zq}+{\overrightarrow{B}}_q$

$=\frac{{\mu }_0}{4\pi }[I_q+I_{2q}+I_{-q}]\frac{1}{a^2}$

$=\frac{{\mu }_0}{4\pi }[qv+2qv+qv]\frac{1}{a^2}$

$\overrightarrow{B_{net}}=\frac{{\mu }_0}{4\pi }\frac{4qv}{a^2}$