Electromagnetic Induction

Multiple Choice

A square loop is placed in a uniform magnetic field perpendicular to the plane of the loop as shown. The loop is 0.50 meters on a side and the magnetic field B has a strength of 2 T. If the loop is rotated through an angle of 90° in 0.1 second what would be the average induced EMF in the loop?

• 0.025 V

• 0.40 V

• 5 V

• 10 V

Multiple Choice

A uniform magnetic field B that is perpendicular to the plane of the page now passes through the loops, as shown. The field is confined to a region of radias a, where a<b, and is changing at a constant rate. The induced emf in the wire loop of radius b is ε. What is the induced emf in the wire loop pf radius 2b?

• zero

• ε/2

• ε

• 2ε

• 4ε

Multiple Choice

Two conducting wire loops move near a very long, straight conducting wire that carries a current I. When the loops are in the positions shown above, they are moving in the directions shown with the same constant speed v. Assume that the loops are far enough apart that they do not affect each other. Which of the following is true about the induced electric currents, if any, in the loops?

• Loop 1

  No current

  Loop 2

  No current

• Loop 1

  No current

  Loop 2

  Counterclockwise

• Loop 1

  Clockwise

  Loop 2

  No current

• Loop 1

  Clockwise

  Loop 2

  Clockwise

• Loop 1

  Counterlockwise

  Loop 2

  Clockwise

Multiple Choice

The magnet shown is initially far away from the conducting loop and is moved at constant speed toward and completely through the loop. If T is the time at which the magnet is halfway through the loop, which of the following graphs best represents the induced current I in the loop as a function of time t ?

Multiple Choice

A metal ring of radius r is placed in a region with a uniform, time-dependent magnetic field that is perpendicular to the plane of the ring. The magnitude of the magnetic field B changes as a function of time t according to the equation B(t) = B₀e^-kt. Which of the following is a correct expression for the magnitude of the electric field induced in the ring as a function of time t?

• ½krB₀

• ½πkr²B₀e^-kt

• (2k/r)B₀e^-kt

• ½krB₀e^-kt

• 2πkr²B₀e^-kt

Multiple Choice

A loop of wire is entering a region that contains a magnetic field of magnitude B with an initial speed of v, as shown in the figure. The graph shows the magnitude of the electric field created in the loop as the loop

enters the field. The electric field creates a counterclockwise current in the loop. Which of the following indicates how the loop is moving as it enters the field and the direction of the magnetic field?

• The loop is moving at a constant speed, and the magnetic field is into the page.

• The loop is moving at a constant speed, and the magnetic field is out of the page.

• The loop is speeding up, and the magnetic field is into the page.

• The loop is speeding up, and the magnetic field is out of the page.

• The loop is slowing down, and the magnetic field is into the page.

  26.

Multiple Choice

A wire loop is rotated in a uniform magnetic field about an axis perpendicular to the field, as shown above. How many times is the induced current in the loop reversed if the loop makes 3 complete revolutions from the position shown?

• One

• Two

• Three

• Six

• Twelve

Multiple Choice

A circular loop of wire in a uniform magnetic field rotates at a constant rotational speed about the axis shown. At time t = 0 the plane of the loop is parallel to the field with point P at the top as shown above left. At time t = t₁ the loop has rotated 180° so that point P is at the bottom as shown above right. Which of the following graphs best represents the magnetic flux through the loop as a function of time t from 0 to t₁ ?