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Concept Questions with Answers

8.01 W11D2

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W11D2 Concept Questions Review

Concept Questions with Answers

8.01 W7D1

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W07D1 Magnetic Dipoles, Force and

Torque on a Dipole, Experiment 2

W07D1 Magnetic Dipoles, Torque and Force on a Dipole, Experiment 2: Magnetic Dipole in a Helmholtz Coil Reading Course Notes: Sections 8.4,8.11.6, 9.5 9.9

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Concept Question: Magnetic Field Lines The picture shows the field lines outside a permanent magnet The field lines inside the magnet point:

1.  Up 2.  Down 3.  Left to right 4.  Right to left 5.  The field inside is zero 6.  I don’t know

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Concept Q. Answer: Magnetic Field Lines

Magnetic field lines are continuous. E field lines begin and end on charges. There are no magnetic charges (monopoles) so B field lines never begin or end

Answer: 1. They point up inside the magnet

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Concept Question: Parallel Wires Consider two parallel current carrying wires. With the currents running in the opposite direction, the wires are

1.  attracted (opposites attract?) 2.  repelled (opposites repel?) 3.  pushed another direction 4.  not pushed – no net force 5.  I don’t know

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Concept Q. Answer: Parallel Wires

I1 creates a magnetic field into the page at wire 2. That makes a force on wire 2 to the right.

I2 creates a magnetic field into the page at wire 1. That makes a force on wire 1 to the left.

Answer: 1. The wires are repelled

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Concept Question: Dipole in Uniform Magnetic Field

From rest, the coil in a uniform magnetic field above will: 1.  rotate wise, not move 2.  rotate counterclockwise, not move 3.  move to the right, not rotate 4.  move to the left, not rotate 5.  move in another direction, without rotating 6.  both move and rotate 7.  neither rotate nor move 8.  I don’t know

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Concept Q. Answer: Dipole in Field

Answer: 1. Coil will rotate clockwise (not move) No net force so no center of mass motion. BUT Magnetic dipoles rotate to align with external field (think compass)

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Concept Question: Dipole in Field

The current carrying coil above will feel a net force

1.  upwards 2.  downwards 3.  of zero 4.  I don’t know 12

Concept Q. Answer: Dipole in Field

Answer: 2. Feels downward force. The forces shown produce a net downward force

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Concept Question: Dipole in Helmholtz

A dipole pointing along the positive x-direction and located at the center of a Helmholtz coil will feel:

1.  a force but not a torque. 2.  a torque but not a force. 3.  both a torque and a force. 4.  neither force nor torque.

Concept Q. Answer: Dipole in Helmholtz

Answer: 2. a torque but not a force. The Helmholtz coil makes a UNIFORM FIELD. Dipole feels only torque (need gradient for force).

Concept Question: Dipole in Anti-Helmholtz Coil

A dipole pointing along the positive z-direction and located at the center of an anti- Helmholtz coil will feel:

1.  a force but not a torque. 2.  a torque but not a force. 3.  both a torque and a force. 4.  neither force nor torque.

Concept Q. Answer: Dipole in Anti-Helmholtz Coil

Answer: 1. A force because there is a non-gradient of the magnetic field but no torque because the magnetic field at the center is zero.

Concept Questions with Answers

8.01 W9D1

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W09D1: Sources of Magnetic Fields:

Ampere’s Law

Today’s Reading Assignment Course Notes: Sections 10.1-10.6

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Concept Question: Line Integral The integral expression

1.  is equal to the magnetic work done around a closed path.

2.  is an infinite sum of the product of the tangent component of the magnetic field along a small element of the closed path with a small element of the path up to a choice of plus or minus sign.

3.  is always zero.

4.  is equal to the magnetic potential energy between two points.

5.  None of the above. 20

C.Q. Answer: Line Integral

2. A line integral by definition is the sum

We need to make a choice of integration direction (circulation) for the line integral. The small line element is tangent to the line and points in the direction of circulation. The dot product therefore is the product of the tangent component of the magnetic field in the direction of the line element. So the answer depends on which way we circulate around the path.

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Concept Question: Ampere’s Law

Integrating B around the loop shown gives us:

1.  a positive number 2.  a negative number 3.  zero

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C.Q. Answer: Ampere’s Law

Answer: 3. Total enclosed current is zero, so

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Concept Question: Ampere’s Law

Integrating B around the loop in the clockwise direction shown gives us:

1.  a positive number 2.  a negative number 3.  zero

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C.Q. Answer: Ampere’s Law

Answer: 2.

Net enclosed current is out of the page, so field is counter-clockwise (opposite to circulation direction)

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Concept Questions with Answers

8.01 W9D2

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W09D2: Faraday’s Law

Today’s Reading Assignment Course Notes: Sections 9.3-9.4, 9.6

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Concept Question: Loop in Uniform Field

While a rectangular wire loop is pulled upward though a uniform magnetic field B field penetrating its bottom half, as shown, there is

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1.  a current in the loop. 2.  no current in the loop. 3.  I do not understand the concepts of current and

magnetic field. 4.  I understand the concepts of current and magnetic field

but am not sure of the answer. 28

Concept Q. Ans.: Loop in Uniform Field

Answer: 1. The motion changes the magnetic flux through the loop. The magnetic flux is decreasing in time as more of the loop enters a region of zero magnetic field. According to Faraday’s Law there is an induced current through the loop.

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Concept Q.: Loop in Uniform Field

While a rectangular wire loop is pulled sideways though a uniform magnetic field B field penetrating its bottom half, as shown, there is

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1.  a current in the loop. 2.  no current in the loop. 3.  I do not understand the concepts of current and

magnetic field. 4.  I understand the concepts of current and magnetic field

but am not sure of the answer. 30

Concept Q. Ans.: Loop in Uniform Field

Answer: 2. The motion does not change the magnetic flux through the loop. The magnetic flux is constant in time. According to Faraday’s Law there is no induced current through the loop.

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Concept Question: Loop

The magnetic field through a wire loop is pointed upwards and increasing with time. The induced current in the coil is

1.  Clockwise as seen from the top 2.  Counterclockwise

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Concept Question Answer: Loop

This produces an “induced” B field pointing down over the area of the loop.

The “induced” B field opposes the increasing flux through the loop – Lenz’s Law

Answer: 1. Induced current is clockwise

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Concept Question: Moving Loop

A circuit in the form of a rectangular piece of wire is pulled away from a long wire carrying current I in the direction shown in the sketch. The induced current in the rectangular circuit is

1.  Clockwise 2.  Counterclockwise 3.  Neither, the current is zero

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Concept Q. Answer: Moving Loop

B due to I is into page; the flux through the circuit due to that field decreases as the circuit moves away. So the induced current is clockwise (to make a B into the page)

Answer: 1. Induced current is clockwise

Note: Iind dl x B force is left on the left segment and right on the right, but the force on the left is bigger. So the net force on the rectangular circuit is to the left, again trying to keep the flux from decreasing by slowing the circuit’s motion

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Concept Question: Faraday’s Law: Loop

A coil moves up from underneath a magnet with its north pole pointing upward. The current in the coil and the force on the coil:

1.  Current clockwise; force up 2.  Current counterclockwise; force up 3.  Current clockwise; force down 4.  Current counterclockwise; force down 36

Concept Question Answer: Faraday’s Law: Loop

The I dl x B force on the coil is a force which is trying to keep the flux through the coil from increasing by slowing it down (Lenz’s Law again).

Answer: 3. Current is clockwise; force is down

The clockwise current creates a self-field downward, trying to offset the increase of magnetic flux through the coil as it moves upward into stronger fields (Lenz’s Law).

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Concept Questions with Answers

8.01 W10D1

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W10D1: Inductance and Magnetic

Field Energy

Today’s Reading Assignment W10D1 Inductance & Magnetic Energy

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Concept Question: Solenoid A very long solenoid consisting of N turns has radius R and length d, (d>>R). Suppose the number of turns is halved keeping all the other parameters fixed. The self inductance

1. remains the same. 2. doubles. 3. is halved. 4. is four times as large. 5. is four times as small. 6. None of the above.

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Concept Q. Ans.: Solenoid Solution 5. The self-induction of the solenoid is equal to the total flux through the object which is the product of the number of turns time the flux through each turn. The flux through each turn is proportional to the magnitude of magnetic field which is proportional to the number of turns per unit length or hence proportional to the number of turns. Hence the self-induction of the solenoid is proportional to the square of the number of turns. If the number of turns is halved keeping all the other parameters fixed then he self inductance is four times as small.