Physics quiz question: loop alongside loop with increasing current

Physics 205B Quiz 6, spring semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 20.27(a)

The current in a circular loop is increasing over time. A square metal loop (with a resistance R) is located alongside the circular loop. The direction of current induced in the square loop is:
(A) clockwise.
(B) counterclockwise.
(C) (No direction, as there is no induced current.)
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (A)

The circular loop is the source of an external magnetic field that creates a flux through square loop, which is the considered the test object. Since the current in the circular loop is increasing, its magnetic field and magnetic flux through the square loop will increase over time, which will create an induced current in the square loop according to Faraday's law.

Everywhere inside of the circular loop, its clockwise current will create a magnetic field that points into the page. Everywhere outside of the circular loop, its current will create a magnetic field that points out of the page. This magnetic field will create a magnetic flux that points out the page through the square loop.

The external magnetic flux through the square loop that points into the page is increasing over time, and from Lenz's law, a current is induced in the square loop that will oppose this change. The square loop will then attempt to create its own magnetic field that points into the page, which means that the induced current in the square loop will be clockwise.

Sections 30882, 30883
Exam code: quiz06Lp4s
(A) : 9 students
(B) : 24 students
(C) : 3 students
(D) : 0 students
(No response: 1 student)

Success level: 24%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.28