A particle of mass m and charge +q is projected with speed v from point P toward an infinite line charge, starting a distance a away. It momentarily stops at point Q located a distance a/2 from the line. If instead a particle of mass m and charge -q is projected from P with the same speed

Question

A particle of mass m and charge +q is projected with speed v from point P toward an infinite line charge, starting a distance a away. It momentarily stops at point Q located a distance a/2 from the line. If instead a particle of mass m and charge -q is projected from P with the same speed v toward the line, its speed at Q is found to be N v / sqrt(2). Find N.

Accepted Answer

2. Let W be the magnitude of the energy associated with moving a charge q from a to a/2. For +q (repelled), it stops: (1/2)mv² = W. For -q (attracted), it gains the same W: (1/2)m v'² = (1/2)mv² + W = mv², so v'² = 2v² and v' = sqrt(2) v = 2v/sqrt(2). Thus N = 2.

Solution

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