Question

two point charges one of 100uC and another of -400uC, are kept 30cm apart. Find the point of zero potential on the line joining the two charges

Answer 1

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Answer 2

Answer:

The point of zero potential on the line joining the two charges is 6 cm from q₁.

Explanation:

Assumption,

Let the point of zero potential on the line joining the two charges be 'x' cm from 100 μC.

Given,

Two point charges (q₁) = 100 μC, and (q₂) = -400 μC, are kept (r) = 30 cm apart.

To find,

The value of 'x'

Concept,

The electric potential of two point charges is given by

$V = \frac{kq}{r}$

Where k = electrostatic constant = 9 × 10⁹ Nm²C⁻²

q = charge of point charge

r = distance between the point charge q and 1C charge.

Calculation,

Potential due to charge q₁ at the point x :

V₁ = kq₁/x

Potential due to charge q₂ at the point (30 - x) :

V₂ = kq₂/(30 - x)

Condition for the zero potential is

V₁ + V₂ = 0

⇒ kq₁/x + kq₂/(30 - x) = 0

⇒ 100 C/x - 400 C/(30 - x) = 0

⇒ 100 C/x = 400 C/(30 - x)

⇒ (30 - x) = 4x

⇒ 30 = 5x

⇒ x = 6 cm.

Therefore, the point of zero potential on the line joining the two charges is 6 cm from q₁.

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