Q: The ninth image shows a surface with a magnetic field passing through it at an angle. What is the correct formula for the magnetic flux $$\phi_B$$ through the surface?

$$\phi_B = \int \vec{B} \cdot d\vec{A} = \int B \cos \theta \, dA$$

Q: A circular loop of radius $$0.10\,\mathrm{m} is $$placed in a uniform magnetic field of $$0.078\,\mathrm{T} at an $$angle of $$25^\circ to $$the normal. What is the magnetic flux through the loop?

$$\phi_B = B A \cos \theta = 0.078 \times \pi (0.10)^2$ \times \cos 25^\circ \approx 0.021\,\mathrm{Wb}$$

Question 1

A solenoid is shown in the first image. If the solenoid has $$N$$ turns, carries a current $$I$$, and has length $$l$$, what is the magnitude of the magnetic field inside the solenoid (assuming it is ideal and long)?

Accepted Answer

$$B = \frac{\mu_0$ N I}{l}$$

Question 2

In the second image, a doorbell circuit is shown. What is the primary function of the iron rod inside the coil when the switch is closed?

Accepted Answer

It increases the magnetic field produced by the coil, making the electromagnet stronger.

Question 3

Ampère’s Law is illustrated in the third image. Which of the following correctly expresses Ampère’s Law for the magnetic field around a closed path enclosing a net current $$I_{enc}$$?

Accepted Answer

$$\sum \vec{B} \cdot d\vec{\ell} = \mu_0$ I_{enc}$$

Question 4

For a long straight wire carrying current $$I$$, what is the magnetic field at a distance $$r$$ from the wire, as shown in the fourth image?

Accepted Answer

$$B = \frac{\mu_0$ I}{2 \pi r}$$

Question 5

In the fifth image, two parallel wires carry equal currents in opposite directions. What is the direction of the magnetic field at point P, which is equidistant from both wires?

Accepted Answer

The magnetic fields from each wire at P are equal in magnitude but opposite in direction, so they cancel and the net field is zero.

Question 6

In the sixth image, two parallel wires carry currents in opposite directions. Using Ampère’s Law, what is the direction of the net magnetic field between the wires?

Accepted Answer

The magnetic fields from each wire add up between the wires, resulting in a stronger field in that region.

Question 7

A coaxial cable is shown in the seventh image. What is the magnetic field outside the cable if the current in the central wire is equal and opposite to the current in the outer braid?

Accepted Answer

The magnetic field outside the cable is zero because the net enclosed current is zero.

Question 8

In the eighth image, a bar magnet is moved into a coil connected to a galvanometer. What is observed and why?

Accepted Answer

A current is induced in the coil, causing the galvanometer to deflect, due to the changing magnetic flux.

Question 9

The ninth image shows a surface with a magnetic field passing through it at an angle. What is the correct formula for the magnetic flux $$\phi_B$$ through the surface?

Accepted Answer

$$\phi_B = \int \vec{B} \cdot d\vec{A} = \int B \cos 	heta \, dA$$

Question 10

In the tenth image, two coils X and Y are wound on an iron ring. When the switch in the X circuit is closed, what happens in coil Y?

Accepted Answer

A current is induced in Y only when the current in X is changing.

Question 11

A circular loop of radius $$0.10\,\mathrm{m} is $$placed in a uniform magnetic field of $$0.078\,\mathrm{T} at an $$angle of $$25^\circ to $$the normal. What is the magnetic flux through the loop?

Accepted Answer

$$\phi_B = B A \cos 	heta = 0.078 	imes \pi (0.10)^2$ 	imes \cos 25^\circ \approx 0.021\,\mathrm{Wb}$$

Question 12

Which of the following best describes electromagnetic induction?

Accepted Answer

The process of generating an emf or current in a conductor by changing the magnetic field through it.

Question 13

A student moves a magnet into a coil as shown in the eighth image. What will increase the induced emf in the coil?

Accepted Answer

Moving the magnet faster into the coil.

Question 14

Which of the following is NOT a valid application of a solenoid or electromagnet?

Accepted Answer

Producing a steady electric field in a vacuum.

Question 15

If the current in a solenoid is doubled, what happens to the magnetic field inside the solenoid?

Accepted Answer

It doubles.

Question 16

A coaxial cable carries a current $$I$$ down the central wire and $$-I$$ back along the outer braid. What is the magnetic field in the region between the two conductors?

Accepted Answer

It is nonzero and can be found using Ampère’s Law for the enclosed current.

Question 17

Which of the following statements about magnetic flux is correct?

Accepted Answer

Magnetic flux depends on the strength of the magnetic field, the area, and the angle between the field and the normal to the surface.

Question 18

A current is induced in a secondary coil only when the current in the primary coil is changing. This is an example of which law?

Accepted Answer

Faraday’s Law of Electromagnetic Induction

Question 19

Which of the following best explains why the magnetic field inside a long solenoid is nearly uniform?

Accepted Answer

The field lines are parallel and closely spaced inside, and the edge effects are negligible for a long solenoid.

Magnetism and Electromagnetic Induction: Solenoids, Ampère’s Law, and Faraday’s Law

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