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Transforming the electric field

  1. Sep 8, 2009 #1
    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.
     
  2. jcsd
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