The figure shows four situations in which charges as indicated (q > 0) are fixed on an axis. In which situation is there a point to the left of the charges where an electron would be in equilibrium ?

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Left of both charges, the electron is attracted by positive charge (rightward) and repelled by negative charge (leftward); the two charges must be of opposite sign for the forces to oppose.

Close to the nearer charge its force dominates; far away the bigger charge dominates. A balance point exists only when the nearer charge has the smaller magnitude.

This holds in (1) (+q nearer, -4q farther) and (2) (-q nearer, +4q farther); it fails in (3) and (4). Hence (A, B).

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