Question

Two particles of charges Q₁ and Q₂ placed at a some distance the force between them is f if the distance between them is reduced to half and charge on each particle is doubled the force between the particles would become?

Answer 1

Step 1: Given

Let Q₁ and Q₂ be charges of two particles and r is distance between them.

Force= f

New force= f'

Then,

Q₁'=2Q₁

Q₂'=2Q₂

r'=r/2

Step 2: Formula used

f=k(Q₁*Q₂)$\frac{1}{r{2}^{}}$

Step 3: Finding new force

f=k(Q₁*Q₂)$\frac{1}{r{2}^{}}$

f'=k(Q₁'*Q₂')$\frac{1}{r^{\prime }{2}^{}}$

f'=k(2Q₁*2Q₂) $\frac{4}{r{2}^{}}$

f'=16k(Q₁*Q₂)$\frac{1}{r^2}$

f'=16 f

New force(f')= 16f

Hence, the new force becomes 16 times the older force.