Midterm2_9HD_2009

# The frame f and the wire move with a velocity v

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(in esu/cm) in the inertial frame F’. The frame F’ (and the wire) move with a velocity v parallel to the direction of the wire with respect to the laboratory frame F. (a) What is the current associated with the wire in its rest frame F’? What are linear charge density and the current in the laboratory frame F? (b) Derive the electric and the magnetic fields at the point (0,0,d) in Cartesian coordinates in F’, the rest frame of the wire. Here d is a constant in cm. (c) Use the Lorentz transformation equations for the fields to find the electric and magnetic fields at the point (0,0,d) in Cartesian coordinates in the laboratory frame F. (d) From the charge density and the current in the lab frame F, calculate the electric and magnetic fields in the lab at (0,0,d). You should obtain the same fields that you found in part (c). (e) Demonstrate explicitly by using the values for the fields at (0,0,d) in both frames that 2 2 B E and B E r r are both relativistic invariants. (f) Suppose that a charge q is at rest at (0,0,d) in frame F’. From the fields, find the total force on the charge q in F’. From the fields, also find the total force on the charge q in the lab frame F. Is the total force larger or

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