Q: The sixth and seventh images show a current-carrying wire bent into a circular arc. What is the formula for the magnetic field at the center O due to the arc of radius $$a$$ and subtending angle $$\theta (in $$radians)?

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

Question 1

The first image shows a medical imaging device. Which physical principle is primarily responsible for the operation of this device?

Accepted Answer

The use of strong magnetic fields and radio waves to align and detect nuclear spins

Question 2

In the second image, a historical experiment is depicted. What fundamental discovery about magnetism and electricity was demonstrated in this experiment?

Accepted Answer

A current-carrying wire produces a magnetic field that can deflect a compass needle

Question 3

The third and fourth images show the direction of the magnetic field at points P and P' due to a current-carrying wire. According to the right-hand rule, what is the direction of the magnetic field at point P if the current is upward?

Accepted Answer

Out of the page

Question 4

The fifth image illustrates the right-hand rule for the cross product. If vector $$\vec{A}$$ points to the right and vector $$\vec{B}$$ points upward, what is the direction of $$\vec{C} = \vec{A} 	imes \vec{B}$$?

Accepted Answer

Into the page

Question 5

The sixth and seventh images show a current-carrying wire bent into a circular arc. What is the formula for the magnetic field at the center O due to the arc of radius $$a$$ and subtending angle $$	heta (in $$radians)?

Accepted Answer

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

Question 6

The eighth, ninth, and tenth images show a circular current loop and the calculation of the magnetic field at a point on its axis. What is the expression for the magnetic field at a distance $$x$$ from the center along the axis of a loop of radius $$a$$ carrying current $$I$$?

Accepted Answer

$$B_x = \frac{\mu_0$ I a^2$}{2(a^2$ + x^2$)^{3/2}$$}$

Question 7

The eleventh and thirteenth images show the magnetic field lines for a current loop and a bar magnet. What similarity do these field patterns illustrate?

Accepted Answer

Both have axially symmetric field lines forming closed loops

Question 8

The fourteenth image shows a wire bent into two semicircles of different radii $$R_1$$ and $$R_2. If $$the current is $$I$$, what is the net magnetic field at the center?

Accepted Answer

$$B = \frac{\mu_0$ I}{4} \left( \frac{1}{R_2$} - \frac{1}{R_1$} \right)$$

Question 9

The fifteenth and sixteenth images show a straight wire and the angles $$\$$theta_1$$ and $$\$$theta_2$$ subtended at point P. What is the general formula for the magnetic field at P due to a finite straight wire?

Accepted Answer

$$B = \frac{\mu_0$ I}{4\pi a} (\sin \$$theta_1$$ - \sin \$$theta_2$$)$$

Question 10

The seventeenth and eighteenth images show the magnetic field lines around a current coming out of and into the page. According to the right-hand rule, what is the direction of the magnetic field lines around a current coming out of the page?

Accepted Answer

Counterclockwise

Question 11

The nineteenth and twentieth images show four wires at the corners of a square, with two currents into and two out of the page. What is the y-component of the magnetic field at the center of the square?

Accepted Answer

$$B_y = 4 B_1$ \sin 45^\circ$$

Question 12

The twenty-first image shows the Earth's magnetic field. What is the most likely source of Earth's magnetic field?

Accepted Answer

Convection currents of charged particles in the liquid outer core

Question 13

The twenty-second image shows two parallel current-carrying wires. What is the force per unit length between two long, parallel wires separated by distance $$a$$ and carrying currents $$I_1$$ and $$I_2$$?

Accepted Answer

$$f = \frac{\mu_0$ I_1$ I_2$}{2\pi a}$$

Question 14

The twenty-third image shows the direction of forces between parallel wires. What is the direction of the force between two parallel wires carrying currents in the same direction?

Accepted Answer

They attract each other

Question 15

The twenty-fourth image shows compass needles around a current-carrying wire. What happens to the compass needles when the current is turned on?

Accepted Answer

They align tangentially to circles centered on the wire

Question 16

The twenty-fifth, twenty-sixth, and twenty-seventh images show a long, straight wire with current $$I$$ and radius $$R. $$What is the magnetic field at a distance $$r \u003c R$$ from the center of the wire?

Accepted Answer

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

Question 17

The twenty-eighth image shows the graph of magnetic field $$B$$ versus distance $$r$$ from the center of a current-carrying wire of radius $$R. $$What happens to $$B as$$ $$r$$ increases from $$0 to$$ $$R$$?

Accepted Answer

$$B$$ increases linearly

Question 18

The twenty-ninth and thirtieth images show a toroid. What is the expression for the magnetic field inside a toroid of $$N$$ turns, carrying current $$I$$, at a distance $$r$$ from the center?

Accepted Answer

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

Question 19

The thirty-first image shows the magnetic field lines inside and outside a solenoid. What is true about the magnetic field inside an ideal solenoid?

Accepted Answer

It is strong and nearly uniform

Sources of the Magnetic Field: Biot–Savart Law, Ampère’s Law, and Applications

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