Question

Charges A and B in FIGURE Q22.14 are equal. Each charge exerts a force on the other of magnitude F. Suppose the charge of B is increased by a factor of 4, but everything else is unchanged. In terms of F,

(a) what is the magnitude of the force on A, and

(b) what is the magnitude of the force on B?

Short answer

a. The magnitude on the force A will increase by a factor $F\left(A\right)=4F$

b. the magnitude of the force on B is same as that of A$F\left(B\right)=4F$

Step-by-step solution

Content Introduction

The sum of all the forces operating on an object is referred to as the magnitude of force. When all of the forces act in the same direction, the force's magnitude increases. When forces act in opposite directions on an object, the amount of the force decreases.

Explanation (Part a)

The electric field strength would decrease.

$$\begin{gathered} E\left(2r\right)\propto \frac{1}{\left(2r^2\right)}=\frac{1}{\left(4r^2\right)} \\ so,\frac{E\left(2r\right)}{E\left(r\right)}=\left[\frac{1}{\left(4r^2\right)}\right].\left[\frac{\left(r^2\right)}{1}\right]=\frac{1}{4} \end{gathered}$$

Therefore, $E\left(2r\right)=\frac{1}{4}(1000N/C)=250N/C$

The magnitude on the force A will increase by a factor$F\left(A\right)=4F$

Explanation (Part b)

By Newton's Third Law, the force of A on B is equal in magnitude to the force of B on A.

Therefore the force on B also increases by a factor of $+4$

$F\left(A\right)=F\left(B\right)=4F$