Q: A proton travels at right angles into a uniform magnetic field of magnitude $$2.50\ \mathrm{T}$$ with a speed of $$1.50 \times 10^7$\ \mathrm{m/s}. $$What is the radius of the proton’s circular orbit in the magnetic field?

$$r = \frac{mv}{qB} = \frac{1.67 \times 10$$^{-27}$$\ \mathrm{kg} \times 1.50 \times 10^7$\ \mathrm{m/s}}{1.6 \times 10$$^{-19}$$\ \mathrm{C} \times 2.50\ \mathrm{T}} = 0.0626\ \mathrm{m}$$

Q: A straight horizontal conductor carrying a current of $$20\ \mathrm{A}$$ from south to north passes through a magnetic field of $$1.5\ \mathrm{T}$$ directed vertically upward. If the field acts over a $$1.2\ \mathrm{m}$$ length of the wire, what is the magnitude of the force on the wire?

$$F = BIL = 1.5\ \mathrm{T} \times 20\ \mathrm{A} \times 1.2\ \mathrm{m} = 36\ \mathrm{N}$$

Q: A particle with charge $$6.40 \times 10$$^{-19}$$\ \mathrm{C}$$ travels in a circular orbit with radius $$4.68\ \mathrm{mm}$$ due to a magnetic field of $$1.65\ \mathrm{T}$$ perpendicular to the orbit. What is the magnitude of the linear momentum $$\vec{p} of $$the particle?

$$p = qBr = 6.40 \times 10$$^{-19}$$\ \mathrm{C} \times 1.65\ \mathrm{T} \times 4.68 \times 10$$^{-3}$$\ \mathrm{m} = 4.94 \times 10$$^{-21}$$\ \mathrm{kg\ m/s}$$

Q: Two long, parallel wires are separated by a distance of $$0.400\ \mathrm{m}. $$The currents $$I_1 = 5.00$$\ \mathrm{A}$$ and I_2$ = 2.00\ \mathrm{A}$$ flow in the same direction. What is the magnitude of the force exerted by each wire on a $$1.20\ \mathrm{m}$$ length of the other?

$$F = \frac{\mu_0$ I_1$ I_2$}{2\pi d} L = \frac{4\pi \times 10$$^{-7}$$\ \mathrm{T\cdot m/A} \times 5.00\ \mathrm{A} \times 2.00\ \mathrm{A}}{2\pi \times 0.400\ \mathrm{m}} \times 1.20\ \mathrm{m} = 6.0 \times 10$$^{-6}$$\ \mathrm{N}$$

Q: A straight wire carrying a current of $$10.0\ \mathrm{A}$$ passes through the center of a cylindrical region with a magnetic field of $$0.850\ \mathrm{T}$$ and a radius of $$3.00\ \mathrm{cm}. $$The wire is perpendicular to both the axis of the region and the magnetic field. What is the magnitude of the force on the wire inside the field?

$$F = BIL = 0.850\ \mathrm{T} \times 10.0\ \mathrm{A} \times 0.060\ \mathrm{m} = 0.51\ \mathrm{N}$$

Q: A wire of length $$2.00\ \mathrm{m}$$ and resistance $$1.00\ \Omega is $$connected to a $$10.00\ \mathrm{V}$$ battery and bent into two parallel pieces, each $$1.0\ \mathrm{m}$$ long, separated by $$0.10\ \mathrm{cm}. A $$second $$1.0\ \mathrm{m}$$ wire of $$1.00\ \Omega is $$connected to a $$5.00\ \mathrm{V}$$ battery and placed parallel at $$0.20\ \mathrm{cm}$$ from the first. What is the magnetic force at point A on the first wire due to the second wire?

$$F = \frac{\mu_0$ I_1$ I_2$}{2\pi d} L = \frac{4\pi \times 10$$^{-7}$$ \times 10 \times 5}{2\pi \times 0.001} \times 1 = 1.0 \times 10$$^{-2}$$\ \mathrm{N}$$

Q: A proton enters a magnetic field at an angle of $$35^\circ to $$the field direction with speed $$1.50 \times 10^7$\ \mathrm{m/s}. $$What is the radius of the helical path?

$$r = \frac{mv \sin \theta}{qB} = \frac{1.67 \times 10$$^{-27}$$ \times 1.50 \times 10^7$ \times \sin 35^\circ}{1.6 \times 10$$^{-19}$$ \times 2.50} = 0.0358\ \mathrm{m}$$

Question 1

A proton travels at right angles into a uniform magnetic field of magnitude $$2.50\ \mathrm{T}$$ with a speed of $$1.50 	imes 10^7$\ \mathrm{m/s}. $$What is the radius of the proton’s circular orbit in the magnetic field?

Accepted Answer

$$r = \frac{mv}{qB} = \frac{1.67 	imes 10$$^{-27}$$\ \mathrm{kg} 	imes 1.50 	imes 10^7$\ \mathrm{m/s}}{1.6 	imes 10$$^{-19}$$\ \mathrm{C} 	imes 2.50\ \mathrm{T}} = 0.0626\ \mathrm{m}$$

Question 2

A straight horizontal conductor carrying a current of $$20\ \mathrm{A}$$ from south to north passes through a magnetic field of $$1.5\ \mathrm{T}$$ directed vertically upward. If the field acts over a $$1.2\ \mathrm{m}$$ length of the wire, what is the magnitude of the force on the wire?

Accepted Answer

$$F = BIL = 1.5\ \mathrm{T} 	imes 20\ \mathrm{A} 	imes 1.2\ \mathrm{m} = 36\ \mathrm{N}$$

Question 3

A particle with charge $$6.40 	imes 10$$^{-19}$$\ \mathrm{C}$$ travels in a circular orbit with radius $$4.68\ \mathrm{mm}$$ due to a magnetic field of $$1.65\ \mathrm{T}$$ perpendicular to the orbit. What is the magnitude of the linear momentum $$\vec{p} of $$the particle?

Accepted Answer

$$p = qBr = 6.40 	imes 10$$^{-19}$$\ \mathrm{C} 	imes 1.65\ \mathrm{T} 	imes 4.68 	imes 10$$^{-3}$$\ \mathrm{m} = 4.94 	imes 10$$^{-21}$$\ \mathrm{kg\ m/s}$$

Question 4

Two long, parallel wires are separated by a distance of $$0.400\ \mathrm{m}. $$The currents $$I_1 = 5.00$$\ \mathrm{A}$$ and I_2$ = 2.00\ \mathrm{A}$$ flow in the same direction. What is the magnitude of the force exerted by each wire on a $$1.20\ \mathrm{m}$$ length of the other?

Accepted Answer

$$F = \frac{\mu_0$ I_1$ I_2$}{2\pi d} L = \frac{4\pi 	imes 10$$^{-7}$$\ \mathrm{T\cdot m/A} 	imes 5.00\ \mathrm{A} 	imes 2.00\ \mathrm{A}}{2\pi 	imes 0.400\ \mathrm{m}} 	imes 1.20\ \mathrm{m} = 6.0 	imes 10$$^{-6}$$\ \mathrm{N}$$

Question 5

A straight wire carrying a current of $$10.0\ \mathrm{A}$$ passes through the center of a cylindrical region with a magnetic field of $$0.850\ \mathrm{T}$$ and a radius of $$3.00\ \mathrm{cm}. $$The wire is perpendicular to both the axis of the region and the magnetic field. What is the magnitude of the force on the wire inside the field?

Accepted Answer

$$F = BIL = 0.850\ \mathrm{T} 	imes 10.0\ \mathrm{A} 	imes 0.060\ \mathrm{m} = 0.51\ \mathrm{N}$$

Question 6

A circular loop of wire of radius $$0.20\ \mathrm{m} is $$placed in a uniform magnetic field of $$2.00\ \mathrm{T}$$, with the area vector parallel to $$\vec{B}. If $$the loop is pulled completely out of the field in $$1.50\ \mathrm{ms}$$, what is the magnitude of the induced emf?

Accepted Answer

$$\mathcal{E} = \frac{\Delta \Phi_B}{\Delta t} = \frac{B \pi r^2$}{\Delta t} = \frac{2.00\ \mathrm{T} 	imes \pi 	imes (0.20\ \mathrm{m})^2$}{1.50 	imes 10$$^{-3}$$\ \mathrm{s}} = 167.6\ \mathrm{V}$$

Question 7

Three parallel wires each of length $$2.50\ \mathrm{m}$$ carry currents $$I_1 = 1.00$$\ \mathrm{A}$$, I_2$ = 3.00\ \mathrm{A}$$, and $$I_3 = 2.00$$\ \mathrm{A}$$, with 2.00$$\ \mathrm{cm}$$ separation between adjacent wires. What is the total magnetic field at point A on the top wire due to the other two wires?

Accepted Answer

$$B = \frac{\mu_0$}{2\pi} \left( \frac{I_2$}{r_{12}} + \frac{I_3$}{r_{13}} ight ) = \frac{4\pi 	imes 10$$^{-7}$$}{2\pi} \left( \frac{3.00}{0.02} + \frac{2.00}{0.04} ight ) = 6.0 	imes 10$$^{-5}$$\ \mathrm{T}$$

Question 8

A wire of length $$2.00\ \mathrm{m}$$ and resistance $$1.00\ \Omega is $$connected to a $$10.00\ \mathrm{V}$$ battery and bent into two parallel pieces, each $$1.0\ \mathrm{m}$$ long, separated by $$0.10\ \mathrm{cm}. A $$second $$1.0\ \mathrm{m}$$ wire of $$1.00\ \Omega is $$connected to a $$5.00\ \mathrm{V}$$ battery and placed parallel at $$0.20\ \mathrm{cm}$$ from the first. What is the magnetic force at point A on the first wire due to the second wire?

Accepted Answer

$$F = \frac{\mu_0$ I_1$ I_2$}{2\pi d} L = \frac{4\pi 	imes 10$$^{-7}$$ 	imes 10 	imes 5}{2\pi 	imes 0.001} 	imes 1 = 1.0 	imes 10$$^{-2}$$\ \mathrm{N}$$

Question 9

A proton enters a magnetic field at an angle of $$35^\circ to $$the field direction with speed $$1.50 	imes 10^7$\ \mathrm{m/s}. $$What is the radius of the helical path?

Accepted Answer

$$r = \frac{mv \sin 	heta}{qB} = \frac{1.67 	imes 10$$^{-27}$$ 	imes 1.50 	imes 10^7$ 	imes \sin 35^\circ}{1.6 	imes 10$$^{-19}$$ 	imes 2.50} = 0.0358\ \mathrm{m}$$

Question 10

What is the angular frequency $$\omega of a $$proton moving in a magnetic field $$B$$?

Accepted Answer

$$\omega = \frac{qB}{m}$$

Question 11

Ampere’s Law is given by which of the following equations?

Accepted Answer

$$\int \vec{B} \cdot d\vec{l} = \mu_0$ I_{enc}$$

Question 12

A straight wire of length $$L$$ carries current $$I$$ perpendicular to a uniform magnetic field $$B. $$What is the expression for the force on the wire?

Accepted Answer

$$F = BIL$$

Question 13

If the direction of current in one of two parallel wires is reversed, what happens to the force between them?

Accepted Answer

The force becomes repulsive.

Question 14

A wire loop of area $$A is $$pulled out of a magnetic field $$B in $$time $$\Delta t. $$What is the induced emf?

Accepted Answer

$$\mathcal{E} = \frac{B A}{\Delta t}$$

Question 15

Which of the following best describes the direction of the force on a positive charge moving perpendicular to a magnetic field?

Accepted Answer

Perpendicular to both the velocity and the magnetic field (right-hand rule).

Study Guidance: Magnetic Fields, Forces, and Motion of Charged Particles

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