A circular loop of radius R carries a clockwise current I1 as shown below. The w

Question

A circular loop of radius R carries a clockwise current I1 as shown below. The wire below the circular

loop carries a current I2 as shown. The center of the horizontal portion of the wire is located a distance 2R

below the center of the loop. The length of the horizontal portion of the wire is 4R.

a.) Use the Law of Biot and Savart to find the net magnetic field at the center of the loop.

b.) A proton is located at the center of the loop and traveling with speed v. What is the force

on the proton if it is traveling into the page?

c. ) A proton is located at the center of the loop and traveling with speed v. What is the force

on the proton if it is traveling to the right?

Note: you must clearly label all quantities used in formulas in the diagram. You must also

clearly explain the direction of each field and force.

Explanation / Answer

(A) B(loop) = µI(loop)/2R at the center B(wire) = µI(wire)/2pD Hence for the net magnetic fields to be zero, then B(loop) = B(wire) µI(loop)/2R = µI(wire)/2pD I(wire) = (pD/R) I(loop) (B) I(wire) is moving to the right, so that B(wire) is pointing down at the center of the loop.

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