Q: The Biot-Savart Law gives the magnetic field $$d\vec{B} at a $$point P due to a current element $$I d\vec{s}. $$Which of the following is the correct mathematical expression for the Biot-Savart Law?

$$d\vec{B} = \frac{\mu_0$}{4\pi} \frac{I d\vec{s} \times \hat{r}}{r^2$}$$

Q: A circular arc of wire of radius $$R$$ subtends an angle $$\theta at $$the center and carries a current $$I. $$What is the magnitude of the magnetic field at the center of the arc?

$$B = \frac{\mu_0$ I \theta}{4\pi R}$$

Question 1

A rectangular current loop of width $$b$$ and length $$a is $$placed in a uniform magnetic field $$\vec{B}$$, as shown in the first image. If the angle between the normal to the loop and the magnetic field is $$	heta$$, what is the magnitude of the torque $$	au on $$the loop?

Accepted Answer

$$	au = IabB \sin 	heta$$

Question 2

The magnetic dipole moment $$\vec{\mu} of a $$current loop is given by which of the following expressions?

Accepted Answer

$$\vec{\mu} = I A \hat{n}$$

Question 3

A moving charge generates a magnetic field. According to the right-hand rule, what is the direction of the magnetic field lines around a positive charge moving into the plane of the page, as shown in the third image?

Accepted Answer

The field lines form circles in a clockwise direction around the charge

Question 4

Which of the following best describes the direction of the magnetic field $$\vec{B} at $$point P, located above a long straight wire carrying current to the right, as shown in the fifth image?

Accepted Answer

Direction A (into the page)

Question 5

The Biot-Savart Law gives the magnetic field $$d\vec{B} at a $$point P due to a current element $$I d\vec{s}. $$Which of the following is the correct mathematical expression for the Biot-Savart Law?

Accepted Answer

$$d\vec{B} = \frac{\mu_0$}{4\pi} \frac{I d\vec{s} 	imes \hat{r}}{r^2$}$$

Question 6

For a long straight wire carrying current $$I$$, what is the magnitude of the magnetic field $$B at a $$distance $$a$$ from the wire?

Accepted Answer

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

Question 7

A circular arc of wire of radius $$R$$ subtends an angle $$	heta at $$the center and carries a current $$I. $$What is the magnitude of the magnetic field at the center of the arc?

Accepted Answer

$$B = \frac{\mu_0$ I 	heta}{4\pi R}$$

Question 8

Ampère’s Law states that the line integral of the magnetic field $$\vec{B}$$ around a closed path is proportional to the total current enclosed by the path. Which equation represents Ampère’s Law?

Accepted Answer

$$\oint \vec{B} \cdot d\vec{s} = \mu_0$ I_{enc}$$

Question 9

Two long, straight wires are oriented perpendicular to the $$xy$$–plane and carry equal currents in opposite directions. At a point equidistant from both wires, what is the direction of the net magnetic field?

Accepted Answer

The net field is along the positive $$y-$$direction

Question 10

A current-carrying loop is placed in a uniform magnetic field. The torque on the loop is zero when:

Accepted Answer

The normal to the loop is parallel to the magnetic field

Question 11

Which of the following statements about the magnetic field produced by a moving charge is correct?

Accepted Answer

The magnetic field lines form concentric circles in planes perpendicular to the velocity of the charge

Question 12

If the current in a long straight wire is doubled, what happens to the magnetic field at a fixed distance from the wire?

Accepted Answer

It doubles

Question 13

A solenoid has $$N$$ turns, length $$l$$, and carries current $$I. $$What is the magnitude of the magnetic field inside the solenoid (far from the ends)?

Accepted Answer

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

Question 14

Which of the following materials is most likely to exhibit ferromagnetism?

Accepted Answer

Iron

Question 15

A wire segment is bent into a circular arc of radius $$R$$ and subtends an angle $$	heta at $$the center. If the current in the wire is $$I$$, what is the direction of the magnetic field at the center of the arc?

Accepted Answer

Perpendicular to the plane of the arc (using the right-hand rule)

Question 16

Which of the following is NOT a correct step when applying Ampère’s Law to find the magnetic field in a symmetric situation?

Accepted Answer

Choose a path where the magnitude of $$B is $$not constant

Question 17

If a current-carrying wire is bent into a loop and placed in a uniform magnetic field, which factor does NOT affect the magnitude of the torque on the loop?

Accepted Answer

The resistance of the wire

Week 7 Lec. 1

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