Question

Two objects, A with charge +Q and B with charge +4Q, are separated by a distance r. The magnitude of the force exerted on the second object by the first is F. If the first object is moved to a distance 2r from the second object, what is the magnitude of the electric force on the second object?

Answer 1

Answer:

The magnitude of electric force on object B due to object A when they are 2r distance apart is F/4.

Explanation:

Given :

Electric charge on object A = +Q

Electric charge on object B = +4Q

When the objects A and B are r distance apart, the magnitude of electrostatic force exerted on B due to A is given by the relation :

$F=\frac{1}{4\pi\epsilon_{0} } \frac{Q\times4Q}{r^{2} }$      .....(1)

Now, the two objects are apart by distance of 2r, hence the force acting on the object B due to A is :

$F_{1} =\frac{1}{4\pi\epsilon_{0} } \frac{Q\times4Q}{(2r)^{2} }$

$F_{1} =\frac{1}{4\pi\epsilon_{0} } \frac{Q\times4Q}{4r^{2} }$

Substitute equation (1) in the above equation.

$F_{1} =\frac{F}{4}$