Question

Given two point charges, Q and 2Q, a distance \(l\) apart, is there a point along the straight line that passes through them where \(E = 0\) when their signs are (a) opposite, (b) the same? If yes, state roughly where this point will be.

Short answer

1. The point is near the charge Q in the opposite direction of the charge 2Q.
2. The point is near the charge Q in the direction of the charge 2Q.

Step-by-step solution

Concepts

The electric field is a vector quantity.

The electric field is zero in a region, where the field due to two charges is opposite.

 Step 2: Explanation

Part (a)

Suppose the charges are opposite in signs. The electric fields due to the charges are in the same directions on the line joining the charges. The field is in the opposite direction outside the charges. As the Q charge is small, the point is near the charge Q in the opposite direction of the charge 2Q.

Part (b)

Suppose the charges are the same in sign. The electric fields due to the charges are in the opposite directions on the line joining the charges. Therefore the field is zero on the line joining the charges. As the Q charge is small, the point is near the charge Q in the direction of the charge 2Q.