Q: A particle with charge $$-5.00\ \text{C}$$ initially moves at $$\vec{v} = (1.00\ \hat{i} + 7.00\ \hat{j})\ \text{m/s}. If it $$encounters a magnetic field $$\vec{B} = 10.00\ \text{T}\ \hat{k}$$, what is the magnetic force vector on the particle? Use $$\vec{F} = q\vec{v} \times \vec{B}.$$

$$(-350\ \hat{i} + 50.0\ \hat{j})\ \text{N}$$

Q: An electron moves perpendicular to a uniform magnetic field of $$3.2 \times 10$$^{-2}$$\ \text{T} in a $$circle of radius $$0.40\ \text{cm}. $$How fast is this electron moving? ($$m_e = 9.11 \times 10$$^{-31}$$\ \text{kg}$$, $$e = 1.60 \times 10$$^{-19}$$\ \text{C}$$, $$v = \frac{eBr}{m})$$

$$2.2 \times 10$$^{7}$$\ \text{m/s}$$

Q: A round loop of diameter $$12\ \text{cm}$$, carrying a current of $$0.40\ \text{A}$$, is placed inside a magnetic field $$\vec{B} = 0.20\ \hat{i} + 0.40\ \hat{j}\ \text{T}. $$The normal to the loop is parallel to $$\hat{n} = -0.60\ \hat{i} - 0.80\ \hat{j}. $$What is the potential energy of the loop? ($$U = -\vec{\mu} \cdot \vec{B}$$, $$\mu = IA)$$

$$+2.0 \times 10$$^{-3}$$\ \text{J}$$

Q: A circular loop of wire of radius $$10\ \text{cm}$$ carries a current of $$6.0\ \text{A}. $$What is the magnitude of the magnetic field at the center of the loop? ($$B = \frac{\mu_0$ I}{2R}$$, $$\mu_0$ = 4\pi \times 10$$^{-7}$$\ \text{T} \cdot \text{m/A})$$

$$3.8 \times 10$$^{-5}$$\ \text{T}$$

Q: The magnetic field of an electromagnetic wave has a peak value of $$5.0 \times 10$$^{-10}$$\ \text{T}. $$What is the intensity of the wave? ($$I = \frac{cB^2$}{2\mu_0$}$$, $$c = 3.0 \times 10^8$\ \text{m/s}$$, $$\mu_0$ = 4\pi \times 10$$^{-7}$$\ \text{T} \cdot \text{m/A})$$

$$3.0 \times 10$$^{-5}$$\ \text{W/m}^2$$

Question 1

A 6.0-μF capacitor is connected in series with a 5.0 MΩ resistor, and this combination is connected across an ideal 15-V DC battery. What is the current in the circuit when the capacitor has reached 20% of its maximum charge? Use $$Q = Q_{max}(1 - e$$^{-t/RC}$$)$$ and $$I = \frac{dQ}{dt}.$$

Accepted Answer

$$2.4\ \mu	ext{A}$$

Question 2

A particle with charge $$-5.00\ 	ext{C}$$ initially moves at $$\vec{v} = (1.00\ \hat{i} + 7.00\ \hat{j})\ 	ext{m/s}. If it $$encounters a magnetic field $$\vec{B} = 10.00\ 	ext{T}\ \hat{k}$$, what is the magnetic force vector on the particle? Use $$\vec{F} = q\vec{v} 	imes \vec{B}.$$

Accepted Answer

$$(-350\ \hat{i} + 50.0\ \hat{j})\ 	ext{N}$$

Question 3

An electron moves perpendicular to a uniform magnetic field of $$3.2 	imes 10$$^{-2}$$\ 	ext{T} in a $$circle of radius $$0.40\ 	ext{cm}. $$How fast is this electron moving? ($$m_e = 9.11 	imes 10$$^{-31}$$\ 	ext{kg}$$, $$e = 1.60 	imes 10$$^{-19}$$\ 	ext{C}$$, $$v = \frac{eBr}{m})$$

Accepted Answer

$$2.2 	imes 10$$^{7}$$\ 	ext{m/s}$$

Question 4

A straight wire that is $$0.60\ 	ext{m}$$ long is carrying a current of $$2.0\ 	ext{A}. It is $$placed in a uniform magnetic field of strength $$0.30\ 	ext{T}. If $$the wire experiences a force of $$0.18\ 	ext{N}$$, what angle does the wire make with respect to the magnetic field? ($$F = ILB\sin	heta)$$

Accepted Answer

$$30^\circ$$

Question 5

A rectangular loop of wire carrying a $$4.0\ 	ext{A}$$ current is placed in a magnetic field of $$0.60\ 	ext{T}. $$The magnitude of the torque acting on this wire when the plane of the loop makes a $$30^\circ$$ angle with the field is measured to be $$1.1\ 	ext{N} \cdot 	ext{m}. $$What is the area of this loop? ($$	au = BIA\sin	heta)$$

Accepted Answer

$$0.53\ 	ext{m}^2$$

Question 6

A round loop of diameter $$12\ 	ext{cm}$$, carrying a current of $$0.40\ 	ext{A}$$, is placed inside a magnetic field $$\vec{B} = 0.20\ \hat{i} + 0.40\ \hat{j}\ 	ext{T}. $$The normal to the loop is parallel to $$\hat{n} = -0.60\ \hat{i} - 0.80\ \hat{j}. $$What is the potential energy of the loop? ($$U = -\vec{\mu} \cdot \vec{B}$$, $$\mu = IA)$$

Accepted Answer

$$+2.0 	imes 10$$^{-3}$$\ 	ext{J}$$

Question 7

Refer to the first image. Two long, parallel wires carry equal currents $$I_1$$ = $$I_2 = 20$$\ 	ext{A}$$ in the directions indicated and are located a distance d = 0.5$$\ 	ext{m}$$ apart. Calculate the magnitude and direction of the magnetic field at the point P$ that is located an equal distance d$ from each wire. ($$\$$mu_0 = 4$$\pi 	imes $$10^{-7}$$\ 	ext{T} \cdot 	ext{m/A}$$)

Accepted Answer

$$8\ \mu	ext{T}$$ upward

Question 8

A circular loop of wire of radius $$10\ 	ext{cm}$$ carries a current of $$6.0\ 	ext{A}. $$What is the magnitude of the magnetic field at the center of the loop? ($$B = \frac{\mu_0$ I}{2R}$$, $$\mu_0$ = 4\pi 	imes 10$$^{-7}$$\ 	ext{T} \cdot 	ext{m/A})$$

Accepted Answer

$$3.8 	imes 10$$^{-5}$$\ 	ext{T}$$

Question 9

A solenoid with 400 turns has a radius of $$0.040\ 	ext{m}$$ and is $$40\ 	ext{cm}$$ long. If this solenoid carries a current of $$12\ 	ext{A}$$, what is the magnitude of the magnetic field near the center of the solenoid? ($$B = \mu_0$ n I$$, $$n = N/L)$$

Accepted Answer

$$15\ 	ext{mT}$$

Question 10

A circular coil of radius $$5.0\ 	ext{cm}$$ and resistance $$0.20\ \Omega is $$placed in a uniform magnetic field perpendicular to the plane of the coil. The magnitude of the field changes with time according to $$B = 0.50e$$^{-20t}$$\ 	ext{T}. $$What is the magnitude of the current induced in the coil at $$t = 2.0\ 	ext{s}$$? ($$\mathcal{E} = -N \frac{d\Phi}{dt}$$, $$I = \frac{\mathcal{E}}{R})$$

Accepted Answer

$$2.6\ 	ext{mA}$$

Question 11

An ideal transformer consists of a 500-turn primary coil and a 2000-turn secondary coil. If the current in the secondary is $$3.0\ 	ext{A}$$, what is the current in the primary? ($$\frac{I_p}{I_s} = \frac{N_s}{N_p})$$

Accepted Answer

$$12\ 	ext{A}$$

Question 12

A $$45\ 	ext{mH}$$ ideal inductor is connected in series with a $$60\ \Omega$$ resistor through an ideal $$15\ 	ext{V} DC $$power supply and an open switch. If the switch is closed at time $$t = 0\ 	ext{s}$$, what is the current $$7.0\ 	ext{ms}$$ later? ($$I = \frac{V}{R}(1 - e$$^{-t/	au}$$)$$, $$	au = L/R)$$

Accepted Answer

$$250\ 	ext{mA}$$

Question 13

Refer to the third image. The $$60\ 	ext{Hz} AC $$source of a series circuit has a voltage amplitude of $$120\ 	ext{V}. $$The resistance, capacitive reactance, and inductive reactance are as shown. What is the rms current in the circuit? ($$I_{rms} = \frac{V_{rms}}{Z}$$, $$Z = \sqrt{R^2$ + (X_L - X_C)^2$})$$

Accepted Answer

$$0.097\ 	ext{A}$$

Question 14

The magnetic field of an electromagnetic wave has a peak value of $$5.0 	imes 10$$^{-10}$$\ 	ext{T}. $$What is the intensity of the wave? ($$I = \frac{cB^2$}{2\mu_0$}$$, $$c = 3.0 	imes 10^8$\ 	ext{m/s}$$, $$\mu_0$ = 4\pi 	imes 10$$^{-7}$$\ 	ext{T} \cdot 	ext{m/A})$$

Accepted Answer

$$3.0 	imes 10$$^{-5}$$\ 	ext{W/m}^2$$

Question 15

The magnitude of the electric field at a point $$P$$ for a certain electromagnetic wave is $$570\ 	ext{N/C}. $$What is the magnitude of the magnetic field for that wave at $$P$$? ($$B = \frac{E}{c}$$, $$c = 3.0 	imes 10^8$\ 	ext{m/s})$$

Accepted Answer

$$1.90\ \mu	ext{T}$$

Question 16

The intensity of solar radiation near the earth is $$1.4\ 	ext{kW/m}^2. $$What force is exerted by solar radiation impinging normally on a $$5.0\ 	ext{m}^2$$ perfectly reflecting panel of an artificial satellite orbiting the earth? ($$F = \frac{2IA}{c}$$, $$c = 3.00 	imes 10^8$\ 	ext{m/s})$$

Accepted Answer

$$47\ \mu	ext{N}$$

Physics II Exam Study Guide: Magnetism, Circuits, and Electromagnetic Waves

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