Question

Two 1.4 g spheres are charged equally and placed 1.7 cm apart. When released, they begin to accelerate at 110 m/s2 .

What is the magnitude of thecharge on each sphere?

Answer 1

Answer:

The magnitude of the charge on each sphere is $7.03\times 10^{-8}\ C$.                                                                      

Explanation:

Given that,

Mass of both spheres, $m=1.4\ g=1.4\times 10^{-3}\ kg$

Separation between spheres, d = 1.7 cm = 0.017 m

When they  released, they begin to accelerate at, $a=110\ m/s^2$

We need to find the magnitude of the charge on each sphere. When they are released, the force due to acceleration is balanced by the electric force between charges as:

$\dfrac{kq^2}{d^2}=ma$

$q=\sqrt{\dfrac{mad^2}{k}}$

$q=\sqrt{\dfrac{1.4\times 10^{-3}\times 110\times (0.017)^2}{9\times 10^9}}$

$q=7.03\times 10^{-8}\ C$

So, the magnitude of the charge on each sphere is $7.03\times 10^{-8}\ C$. Hence, this is the required solution.