Charge in a Magnetic Field question

Lonewolf393 · Dec 6, 2016

Homework Statement

Physics exam question with a circular loop of charges around a time-varying magnetic field B_z(t) = B0 + B1 t/T, with answer choices A through E giving forces on charge q in i and j directions, plus a diagram of a loop with a coordinate axis and a magnet moving near a coil.

Two diagrams of a circular loop with a charge q inside, with a time-varying magnetic field pointing out of the paper, and induced electric field arrows around the loop; a coordinate axis shows z out of the paper, x to the right, y up. Multiple-choice answer options A through E for the force are printed above.

These are two similar questions, one from my previous exam and one from a sample test my teacher provided. I understand how to work the problem, but my question is how is the i or j component decided in each of these?

Homework Equations

From our formula sheet...

The Attempt at a Solution

Handwritten derivation on a printed answer key: dE/dt equals minus B0/T times the area 2πr², then E(2πr) = B0/T(πr²), giving E = B0 r/(2T), and f = a B0 r/(2T).

kuruman · Dec 6, 2016

There is a coordinate system provided that gives the direction of the unit vectors. The direction of the force on charge q (assuming it is positive) is the same as the direction of the induced current at the position of the charge if the dotted circle were a circular metal loop. The induced current can either be clockwise or counterclockwise. This eliminates all the ## \hat{j}## options in the first picture and all the ##\hat{i}## options in the second picture. The sign depends on whether you have clockwise or counterclockwise current flow. Can you figure that out?

Charge in a Magnetic Field question

Homework Statement

Homework Equations

The Attempt at a Solution

Discussion

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