Two long straight wires carrying a large conventional currentI are connected by

Question

Two long straight wires carrying a large conventional currentI are connected by one-and-a-quarter turns of wire of radius R. Anelectrons moving to the right with speed v at the instant taht itpasses through the center of the arc.You apply an electric field Eat the center of the arc in susch a way that the net force on theelectron at this instant is zero, which is easily shown to benegligible, and the magnetic field of the coil is much larger thanthe magnetic field of the Earth.) An electron moves to the right at the center of the arc. Determine the direction and magnitude of the electric field E.Be sure to explain your work fully; draw and label any vectors youuse.

Explanation / Answer

The magnetic field B at the center due to 2 straight lines is zero.the field B at the center due to current I of the one-and-a-quarterturns of wire of radius R is (1/4)*0I/(2R) = 0I/(8R) with the direction into the page. (Thedrawing of the question is wrong, I assume the direction of thecurrent of the vertical line is downward) The magnetic force on the electron is qv x B. So the electric force on it is qE. The net force is q(qv x B + E) = 0 E = -v x B magnitude of E = vB = 0Iv/(8R) direction of E is that of -v x B, that is downward.

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