Question

Positive point chages $q=+8.00\mu C$ and $q^{\prime }=+3.00\mu C$ are moving relative to an observer at point $P$, as shown in the figure. the distance $d$ is $0.120$ $m$. When the two charges are at the locations as shown in the figure, what are the magnitude and direction of the net magnetic field they produce at point $P$?
(Take $v=4.50\times {10}^{6}m{s}^{-1}$ and $v^{\prime }=9.00\times {10}^{6}m{s}^{-1}$).

• A. $4.38\times {10}^{-4}$ $T$, into the page
• B. $4.38\times {10}^{-4}$ $T$, out of the page
• C. $2.16\times {10}^{-4}$ $T$, into the page
• D. $2.9\times {10}^{-9}$ $T$, out of the page

Answer 1

Answer: (A)

$4.38\times {10}^{-4}$ $T$, into the page

$B_{total}=B+B^{\prime }=\frac{{\mu }_0}{4\pi }(\frac{qv}{d^2}+\frac{q^{\prime }{v}^{\prime }}{d^2})$
$B=\frac{{\mu }_0}{4\pi }(\frac{(8.0\times {10}^{-6}C)(4.5\times {10}^6{ms}^{-1})}{{\left(0.120m\right)}^2}+\frac{(3.0\times {10}^{-6}C)(9.0\times {10}^6{ms}^{-1})}{{\left(0.120m\right)}^2})$
$B=4.38\times {10}^{-4}T$
Direction is into the page.