PHYS 142 Lecture Notes - Lecture 26: Electric Field

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12 Mar 2015

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Phys 142: electromagnetism and optics - lecture 26: lenz"s law, faraday"s law, and induced fields. There is an induced current in a closed conducting loop, if and only if the magnetic flux through the loop is changing. The direction of the induced current is such that the induced magnetic field opposes the change in flux. Example: pushing a bar magnet (north face) into a circular loop. This causes the magnetic flux to increase in the downward direction (from south face to north face) To oppose this change in flux, the loop itself generates an induced magnetic field binduced that now points in the upward direction. Thus, using the right hand rule, the current in the loop moves in a counter clockwise direction (since. When the magnet stops moving, there is no longer any change in flux, and thus no more induced current in the loop.

Related Questions

A loop of wire is lying flat on a tabletop. A uniform magneticfield is directed vertically UPWARDS such that it is perpendicularto the tabletop (and the loop) and pointing toward the ceiling.Beyond the edges of the table, the magnetic field is zero. Imaginethat you are looking DOWN on the loop from above. Which of thefollowing statements are true about the induced EMF in the wireloop?

1)If the magnetic field suddenly decreases, the induced currentwill be in a counter-clockwise direction.
2)If the magnetic field suddenly decreases, the induced currentwill be in a clockwise direction.
3)If the loop suddenly shrinks in size, the induced current will bein a clockwise direction.
4)If you pull the loop out of the field, by sliding it off thetable, the induced current will be in a clockwise direction.
5)Lenz's Law states that the induced current always leads to amagnetic field that OPPOSES the change in magnetic flux.
6)If you keep the loop on the table, but pull it to the right,there will be no induced current.

you hold a wire coil so that the plane of the coil is perpendicular to a magnetic field b⃗ .

A circular loop of wire lies flat on a level tabletop. A bar magnet is held stationary above the circular loop with its north pole point downward. As viewed from above, in what direction does the induced current flow in the loop of wire?
1. No current is induced in the loop of wire.
2. An induced current flows clockwise in the loop of wire.
3. An induced current flows counterclockwise in the loop of wire.
4. The direction of the induced current cannot be determined from the given information.

redweasel197

You are given a circular conducting wire loop with one
end cut out and connected to a resistor, R, as shown in
the figure to the right. A metal rod of length l is set at an
initial angle ?0 from the resistor, and then rotates
clockwise about the center of the wire loop with angular
frequency through a uniform magnetic field B
directed into the page. The metal rod stays in contact
with the wire loop at all points of its motion. Unless
otherwise requested, all answers should be in simplified
algebraic form using the above given variables.

(a) Given that the initial angle ?0 is in radians, what is theinitial area of the closed circuit âwedgeâdefined by ?0? (2pts.)
(b) What is the magnetic flux through this initial âwedgeâ areadefined by ?0? (2 pts.)
Starting at time t=0 at position ?0, the rod is rotated clockwisewith angular velocity as shown in
the figure. Given this configuration, answer questions (c)-(g)below:
(c) What is the direction of the induced magnetic field inside theâwedgeâ? (2 pts)
(d) What is the direction of the induced current around the closedcircuit? (2 pts)
(e) What is the magnitude of the induced emf, E in the circuit? (4pts)
(f) What is the magnitude of the induced current in the circuit? (4pts)
(g) What is the power used by the resistor? (4 pts)
(h) The metal rod is now rotated in the opposite direction, i.e. inthe counter-clockwise direction. Given this information, completethe chart below as to what quantities you just calculated change,and what ones do not change. You do not have to show work, justgive the result. No partial credit will be given here. (5pts)

Direction of induced magnetic field inside the âwedgeâ.
Direction of the induced current around the closed circuit.
Magnitude of the induced emf, E in the circuit.
Magnitude of the induced current in the circuit.
Power used by the resistor.

The setup is now modified slightly so that the circular conductingwire loop no longer has a small
section removed as shown in both figures below. This modificationwould allow the metal rod to
continuously rotate on the circular wire loop as clearlyillustrated in the 3D side view. The metal rod
is rotated clockwise, as in the initial part of the problem.

(i) Given this information, complete the chart below. You do nothave to show work, just give the
result. No partial credit will be given here. (5 pts)

Direction of induced magnetic
field inside the âwedgeâ.
Direction of the induced current
around the closed circuit.
Magnitude of the induced emf, E in
the circuit.
Magnitude of the induced current
in the circuit.
Power used by the resistor.

PHYS 142 Lecture Notes - Lecture 26: Electric Field

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