Q: Given a wire bent into two arcs of radii $$a$$ and $$b ($$with $$a \u003c b$$), both subtending an angle $$ heta at $$the center $$O$$, carrying current $$I$$, what is the magnitude of the net magnetic field at $$O$$? (Assume the straight segments do not contribute.)

$$B = \frac{\mu_0$ I \theta}{4\pi} \left( \frac{1}{a} - \frac{1}{b} \right)$$

Question 1

A wire is bent into the shape shown in the figure, with two circular arcs joined by straight segments. If the wire carries a current $$I$$ uniformly throughout its length, what is the direction of the magnetic field at the center $$O of $$the arcs?

Accepted Answer

The magnetic field at $$O is $$the vector sum of the fields due to each arc, and the straight segments do not contribute at $$O.$$

Question 2

Given a wire bent into two arcs of radii $$a$$ and $$b ($$with $$a \u003c b$$), both subtending an angle $$	heta at $$the center $$O$$, carrying current $$I$$, what is the magnitude of the net magnetic field at $$O$$? (Assume the straight segments do not contribute.)

Accepted Answer

$$B = \frac{\mu_0$ I 	heta}{4\pi} \left( \frac{1}{a} - \frac{1}{b} ight)$$

Question 3

If the angle subtended by each arc in the bent wire is $$	heta = \frac{\pi}{2}$$, the current is $$I$$, and the radii are $$a$$ and $$b$$, what is the direction of the net magnetic field at $$O$$?

Accepted Answer

The field points out of the page.

Question 4

A long straight wire carries a current $$I$$, and a nearby rectangular loop carries a clockwise current $$i. $$What is the direction of the net force on the loop due to the wire?

Accepted Answer

The net force is repulsive; the loop is pushed away from the wire.

Question 5

For the rectangular loop near the straight wire, which side of the loop experiences the greatest force due to the wire's magnetic field?

Accepted Answer

The side closest to the wire ($$l_1).$$

Question 6

If the current in the straight wire is reversed, what happens to the direction of the net force on the rectangular loop?

Accepted Answer

The direction of the net force on the loop is reversed.

Question 7

Which equation gives the magnetic field at a distance $$r$$ from a long straight wire carrying current $$I$$?

Accepted Answer

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

Question 8

A rectangular loop of width $$w$$ and length $$l is $$placed parallel to a long straight wire at a distance $$d$$ from the wire. If the loop carries current $$i$$ and the wire carries current $$I$$, what is the expression for the net force on the loop?

Accepted Answer

$$F = \frac{\mu_0$ I i l}{2\pi} \left( \frac{1}{d} - \frac{1}{d + w} \right)$$

Question 9

If the rectangular loop is moved farther from the straight wire, what happens to the magnitude of the net force on the loop?

Accepted Answer

The magnitude of the net force decreases.

Question 10

If the current in the loop is reversed, but the current in the wire remains the same, what happens to the direction of the net force on the loop?

Accepted Answer

The direction of the net force is reversed.

Question 11

Which physical law is primarily used to calculate the magnetic field produced by a current-carrying wire at a point in space?

Accepted Answer

Biot-Savart Law

Question 12

A wire is bent into a circular arc of radius $$R$$ subtending an angle $$	heta at $$the center. What is the magnetic field at the center due to the arc?

Accepted Answer

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

Question 13

If the rectangular loop is replaced by a circular loop of radius $$r$$ near the straight wire, how does the net force on the loop compare to the rectangular case?

Accepted Answer

The net force depends on the geometry, but the principle of superposition of forces from each segment applies.

Question 14

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

Accepted Answer

The magnetic field increases proportionally.

Question 15

Which of the following best describes the force between two parallel wires carrying currents in the same direction?

Accepted Answer

The wires attract each other.

Question 16

A student claims that the straight segments of the bent wire contribute to the magnetic field at the center $$O. Is $$this correct?

Accepted Answer

No, the straight segments do not contribute to the field at $$O$$ because their distance from $$O is $$zero.

Magnetic Field of Currents and Loops: Physics 10220 Tutorial 7 Study Notes

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