Midterm2_9HD_2009

# From the fields also find the total force on the

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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 smaller in F than in F’? Is the answer what you have expected if you had transformed the force? Lorentz transformation equations for fields, with primed quantities measured in frame F’ moving in +x direction with speed v as seen from F. x x E E = ) ( z y y B E E β γ = ) ( y z z B E E β γ + = x x B B = ) ( z y y E B B β γ + = ) ( y z z E B B β γ = Note :To find unprimed fields in terms of the primed fields, exchange the primed and unprimed quantities, and change the sign of β in the equations. 3. (20 points) (a) Consider a wire of radius b (in cm), with its center lying along the x-axis. There is a current density J =Ar 2 (in esu/(sec-cm 2 ) along the wire in cylindrical coordinates, for 0 r b. Find the magnetic field both inside and outside the wire. (b) Suppose that another wire has current I (in esu/sec) and negligible cross-section. It is parallel to the first wire over length L (in cm) and located distance d (in cm) from the center of the first wire, where d>b. Find the force acting on the second wire, assuming that the two currents flow in opposite directions. By

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