Question

A negative charge of -0.550 µC exerts an upward 0.600-N force on an unknown charge that is located 0.300 m directly below the first charge. What are (a) the value of the unknown charge (magnitude and sign); (b) the magnitude and direction of the force that the unknown charge exerts on the -0.550 µC charge?

Answer 1

Answer:

(a). The unknown charge is 10.9 μC.

(b). The magnitude of the force that the unknown charge exerts on the charge of magnitude 0.550 μC is 0.600 N and direction is downward

Explanation:

Given that,

Charge = -0.550μC

Force = 0.600 N

Distance = 0.300 m

(a). We need to calculate the unknown charge

Using formula of force

$F=\dfrac{1}{4\pi\epsilon_{0}}\times\dfrac{q_{1}q_{2}}{r^2}$

Put the value into the formula

$0.600=\dfrac{9\times10^{9}\times0.550\times10^{-6}\timesq_{2}}{(0.300)^2}$

$q_{2}=\dfrac{0.600\times(0.300)^2}{9\times10^{9}\times0.550\times10^{-6}}$

$q_{2}=10.9\times10^{-6}\ C$

$q_{2}=10.9\ \mu C$

(b). We need to calculate the magnitude and direction of the force that the unknown charge exerts on the -0.550 µC charge

The force between the charges is same,force exerted by q₁ on q₂ is equal to force exerted by q₂ on q₁ but direction is opposite.

The magnitude of the force that the unknown charge exerts on the charge of magnitude 0.550 μC is 0.600 N and direction is downward

Hence, (a). The unknown charge is 10.9 μC.

(b). The magnitude of the force that the unknown charge exerts on the charge of magnitude 0.550 μC is 0.600 N and direction is downward