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Electric Charges And Fields

Question

The charges on two spheres are + 7 µC and -5C respectively. They experience a force F. If each of them is given an additional charge of -2 µC, then the new force of attraction will

F

$\frac{F}{2}$

$\frac{F}{\sqrt{3}}$

2F

Solution

Given:-

q₁ = + 7gµC = +7 X 10^-6 C

q₂= -5 μC = -5 × 10^-6 C

New force F'= ?

We know that,

F = $\frac{1}{4 π ε_{0}} . \frac{q_{1} q_{2}}{r^{2}}$

F = $\frac{1}{4 π ε_{0}} \frac{(+ 7 + 10^{- 6}) (- 5 \times 10^{- 6})}{r^{2}}$

= $- \frac{1}{4 {πε}_{0}} \frac{35 \times 10^{- 12}}{r^{2}}$ N

F' = $\frac{1}{4 {πε}_{0}} \frac{(+ 5 \times 10^{- 6}) (- 7 \times 10^{- 6})}{r^{2}}$

= $- \frac{1}{4 {πε}_{0}} \frac{35 \times 10^{- 12}}{r^{2}}$ N

⇒ F' = F