Question

Given two charges q1 and q2. Both are positive and q2 is three times as large as q1. Additionally there is given a test charge q0 which is placed in between charge q1 and q2. Where has the charge to be placed so that the net force on the test charge is zero?

Answer 1

Answer:

Explanation:

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Answer 2

q₀ has to be placed at r/(1+√3) from q₁ so that the net force on the test charge is zero.

Given:

q₁ = c

q₂ = 3c

q₀ is the test charge between q1 and q2

To Find:

The distance at which q₀ is placed so that the net force is zero.

Solution:

If the net force on q₀ is zero then three charges must be in equilibrium

F1 = F2 but in opposite direction

where F1 is the force between q₀ and q₁

F2 is the force between q₀ and q₂

We know that F = kq₁q₂/r²

F1 = kq₀c/x²

F2 = kq₀3c/(r-x)²

On equating both F1 and F2 we get,

kq₀c/x² = kq₀3c/(r-x)²

1/x² = 3/(r-x)²

Taking square root on both sides we get,

1/x = √3/r-x

r-x = √3x

x(1+√3) = r

x = r/(1+√3)

Therefore, q₀ has to be placed at r/(1+√3) from q₁ so that the net force on the test charge is zero.

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