A charge q is divided into two parts q₁, and (q – q₁) what is the ratio of q/q₁ so that the force between the two parts placed a given distance apart is maximum?

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Question

This question was previously asked in

PGCIL DT Electrical 22 Aug 2021 Official Paper (NR III)

Answer 1

Concept: Given one part of the charge is q₁. Thus other part of the charge is q - q₁.

From Columb's law:

Electrostatic force b/w them,

or,

where = 9 × 10⁹ = constant

r = distance between two charges

For maximum charge

∴ = 0

or, = 0

or, q - 2q₁ = 0

or, q = 2q₁

or, q₁ =

∴ q - q₁ = q -

∴ Force b/w them is maximum if the two parts have equal change each.

∴ The ratio of = 2 ∶ 1

Therefore, current option is 2.