# Transforming the electric field

1. Sep 8, 2009

### jason12345

Suppose I have two charges of mass m'_c stationary in S' separated by a constant distance and one of the charges is released at time t' and accelerates with acceleration _a' to a velocity du' a time dt' later. The force is then just m'_c*du'/dt'. If I transform this event to frame S, then the velocity is transformed using the addition of velocities formula and dt' is transformed using the LT giving:

du = (V + du')/(1 + Vdu'/c^2) - V

dt = gamma(dt' + dx'V/c^2)
= gamma(dt' + 1/2 _a dt'^2 V/c^2)
= gamma dt'.

So the acceleration in S is:

((V + du')/(1 + Vdu'/c^2) - V)/gamma

Is this correct so far?

I need to transform m'_c to m_c to work out the equivalent force in S causing the moving charge to accelerate. How do I do this?

How do I work out the force on a stationary charge in S placed at the point where the accelerating charge is?

Thanks for your interest.

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