First slide

Electrostatic force

Question

Three charges 4q, Q and q are in a straight line in the position of 0, l/2 and l respectively. The resultant force on q will be zero, if Q =

Easy

A

– q
B

– 2q
C

– $\frac{q}{2}$
D

4q

Solution

The force between 4q and q; $F_{1} = \frac{1}{4 {πε}_{0}} \cdot \frac{4 q \times q}{l^{2}}$
The force between Q and q; $F_{2} = \frac{1}{4 {πε}_{0}} \cdot \frac{Q \times q}{{(l / 2)}^{2}}$
We want $F_{1} + F_{2} = 0$ or $\frac{4 q^{2}}{l^{2}} = - \frac{4 Qq}{l^{2}} \Rightarrow Q = - q$

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