Answer to Question #161899 in Electricity and Magnetism for Mel

Question

Two point charges are located on the y-axis of a  coordinate system: q1 = −3.0 nC is at y = −2.0 cm, and q2 = 1.0 nC is at y = −4.0 cm. What is the total electric force exerted by q1 and q2 on a charge q3 = 5.0 nC at y = 0?

Answer 1

As per the given question,

$q_1=-3.0nC=3\times 10^{-9}C$

position co-ordinate $y_1=-2.0cm=-0.02m$

$q_2=1\times 10^{-9}C$

$y_2=-4.0cm = -0.04m$

$q_3=5\times 10^{-9}C$

$y_3=0$

So, net force on the charge $q_3$

$F_{net}=\frac{q_1q_3}{4\pi (y_3-y_1)^2}-\frac{q_2q_3}{4\pi (y_3-y_2)^2}$

Now, substituting the values,

$F_{net}=\frac{3\times 10^{-9}\times5\times10^{-9}\times 9\times 10^9}{(0.02-0)^2}+\frac{1\times 10^{-9}\times5\times10^{-9}\times 9\times 10^9}{(0.04-0)^2}$

$=\frac{135\times 10^{-9}}{4\times 10^{-4}}+\frac{45\times 10^{-9}}{16\times 10^{-4}}$

$=\frac{(540+45)\times 10^{-5}}{16}N$

$=\frac{595\times 10^{-5}}{16}N$

$=37.18\times 10^{-5}N$