Electromagnetism and Waves - Final Exam

Inductor with constant current i flowing from a to b

no potential difference

A planar electromagnetic wave is propagating in the +x direction. At a certain point P and at a given instant, the electric field of the wave is given by E= (0.082 V/m) ĵ. What is the magnetic vector of the wave at the point P at that instant? (c = 3.0 x 10^8 m/s) A) 0.27 nT k B) -0.27 nT k C) 0.27 nT ĵ D) 6.8 nT k E) -6.8 nT ĵ

A) 0.27 nT k

The magnitude of the magnetic field at point P for a certain electromagnetic wave is 2.12 μT. What is the magnitude of the electric field for that wave at P? (c = 3.0 x 10^8 m/s) A) 636 N/C B) 745 N/C C) 5.23 µN/C D) 6.36 µN/C E) 7.45 µN/C

A) 636 N/C

A circular metal ring is situated above a long straight wire, as shown in the figure. The straight wire has a current flowing to the right, and the current is increasing in time at a constant rate. Which statement is true? A) There is an induced current in the metal ring, flowing in a clockwise direction. B) There is an induced current in the metal ring, flowing in a counter-clockwise direction. C) There is no induced current in the metal ring because the current in the wire is changing at a constant rate.

A) There is an induced current in the metal ring, flowing in a clockwise direction

The figure shows a bar magnet moving vertically upward toward a horizontal coil. The poles of the bar magnets are labeled X (top) and Y (bottom). As the bar magnet approaches the coil it induces an electric current in the direction indicated on the figure (counter-clockwise as viewed from above). What are the correct polarities of the magnet? A) X is a south pole, Y is a north pole. B) X is a north pole, Y is a south pole. C) Both X and Y are north poles. D) Both X and Y are south poles. E) The polarities of the magnet cannot be determined from the information given.

A) X is a south pole, Y is a north pole.

In the figure, a bar magnet moves away from the solenoid to the left. The induced current through the resistor R is A) from left to right. B) from right to left. C) There is no induced current through the resistor.

A) from left to right.

An electromagnetic wave is propagating towards the west. At a certain moment the direction of the magnetic field vector associated with this wave points vertically up. The direction of the electric field vector of this wave is: A) horizontal and pointing south. B) vertical and pointing down. C) horizontal and pointing north. D) vertical and pointing up. E) horizontal and pointing east.

A) horizontal and pointing south.

A flexible loop of wire lies in a uniform magnetic field of magnitude B directed into the plane of the picture. The loop is pulled as shown, reducing its area. The induced current A. flows downward through resistor R and is proportional to B. B. flows upward through resistor R and is proportional to B. C. flows downward through resistor R and is proportional to B2 . D. flows upward through resistor R and is proportional to B2 . E. none of the above

A. flows downward through resistor R and is proportional to B.

A circular loop of wire is in a region of spatially uniform magnetic field. The magnetic field is directed into the plane of the figure. If the magnetic field magnitude is decreasing, A. the induced emf is clockwise. B. the induced emf is counterclockwise. C. the induced emf is zero. D. The answer depends on the strength of the field

A. the induced emf is clockwise.

A current i flows through an inductor L in the direction from point b toward point a. There is zero resistance in the wires of the inductor. If the current is decreasing, A. the potential is greater at point a than at point b. B. the potential is less at point a than at point b. C. The answer depends on the magnitude of di/dt compared to the magnitude of i. D. The answer depends on the value of the inductance L. E. both C. and D. are correct.

A. the potential is greater at point a than at point b.

An inductor has a current I(t) = (0.500 A) cos[(275 s-1 )t] flowing through it. If the maximum emf across the inductor is equal to 0.500 V, what is the self-inductance of the inductor? A) 4.37 mH B) 3.64 mH C) 2.75 mH D) 0.73 mH E) 1.43 mH

B) (.500 V)/(-.500*275*sin(275)) = 3.64 mH

The magnitude of the electric field at a point P for a certain electromagnetic wave is 570 N/C. What is the magnitude of the magnetic field for that wave at P? (c = 3.0 x 10^8 m/s) A) 2.91 µT B) 1.90 µT C) 1.10 µT D) 1.41 µT E) 2.41 µT

B) 1.90 µT

Given that the wavelengths of visible light range from 400 nm to 700 nm, what is the highest frequency of visible light? (c = 3.0 x 10^8 m/s) A) 3.1 × 10^8 Hz B) 7.5 × 10^14 Hz C) 2.3 × 10^20 Hz D) 4.3 × 10^14 Hz E) 5.0 × 10^8 Hz

B) 7.5 × 10^14 Hz

An inductor (inductance L) and a capacitor (capacitance C) are connected as shown. If the values of both L and C are doubled, what happens to the time required for the capacitor charge to oscillate through a complete cycle? A. It becomes 4 times longer. B. It becomes twice as long. C. It is unchanged. D. It becomes 1/2 as long. E. It becomes 1/4 as long.

B. It becomes twice as long.

The rectangular loop of wire is being moved to the right at constant velocity. A constant current I flows in the long wire in the direction shown. What are the directions of the magnetic forces on the left-hand (L) and right-hand (R) sides of the loop? A. L: to the left; R: to the left B. L: to the left; R: to the right C. L: to the right; R: to the left D. L: to the right; R: to the right

B. L: to the left; R: to the right

In a sinusoidal electromagnetic wave in a vacuum, the magnetic energy density A. is the same at all points in the wave. B. is maximum where the electric field has its greatest value. C. is maximum where the electric field is zero. D. none of the above

B. is maximum where the electric field has its greatest value.

In an L-R-C series circuit as shown, suppose that the angular frequency of the ac source equals the resonance angular frequency. In this case, the circuit impedance A. is maximum. B. is minimum, but not zero. C. is zero. D. is neither a maximum nor a minimum. E. could be anything; not enough information is given to decide.

B. is minimum, but not zero.

A sinusoidal electromagnetic wave in a vacuum is propagating in the positive z-direction. At a certain point in the wave at a certain instant in time, the electric field points in the negative x-direction. At the same point and at the same instant, the magnetic field points in the A. positive y-direction. B. negative y-direction. C. positive z-direction. D. negative z-direction. E. none of the above

B. negative y-direction.

In the transformer shown in the drawing, there are more turns in the secondary (N2 ) than in the primary (N1 ). In this situation, the voltage amplitude is A. greater in the primary than in the secondary. B. smaller in the primary than in the secondary. C. the same in the primary and in the secondary. D. dependent on the frequency of the ac source. E. dependent on the precise values of N1 and N2 .

B. smaller in the primary than in the secondary.

In an L-R-C series circuit as shown, the current has a very small amplitude if the ac source oscillates at a very high frequency. Which circuit element causes this behavior? A. the resistor R B. the inductor L C. the capacitor C D. Two of these elements acting together are necessary. E. Misleading question—the current actually has a very large amplitude if the frequency is very high.

B. the inductor L

What is the self-inductance of a solenoid 30.0 cm long having 100 turns of wire and a cross-sectional area of 1.00 × 10-4 m2? (μ0 = 4π × 10-7 T ∙ m/A) A) 4.19 nH B) 4.19 pH C) 4.19 µH D) 4.19 mH E) 4.19 H

C) (4*pi*10^(-7)*100^2*(1*10^(-4)))/(30*10^(-2)) = 4.19 µH

If the magnetic field of an electromagnetic wave is in the +x-direction and the electric field of the wave is in the +y-direction, the wave is traveling in the: A) xy-plane. B) +z-direction. C) -z-direction. D) -x-direction. E) -y-direction.

C) -z-direction.

A circular loop of wire lies in the plane of the paper. An increasing magnetic field points out of the paper. What is the direction of the induced current in the loop? A) counter-clockwise then clockwise B) clockwise then counter-clockwise C) clockwise D) counter-clockwise E) There is no current induced in the loop

C) clockwise

In an electromagnetic wave, the electric and magnetic fields are oriented such that they are: A) parallel to one another and perpendicular to the direction of wave propagation. B) parallel to one another and parallel to the direction of wave propagation. C) perpendicular to one another and perpendicular to the direction of wave propagation. D) perpendicular to one another and parallel to the direction of wave propagation.

C) perpendicular to one another and perpendicular to the direction of wave propagation.

An L-R-C series circuit as shown is operating at its resonant frequency. At this frequency, how are the values of the capacitive reactance X_C , the inductive reactance X_L , and the resistance R related to each other? A. X_L = R; X_C can have any value. B. X_C = R; X_L can have any value. C. X_C = X_L ; R can have any value. D. X_C = X_L = R E. None of the above is correct.

C. X_C = X_L ; R can have any value.

An inductance L and a resistance R are connected to a source of emf as shown. When switch S1 is closed, a current begins to flow. The time required for the current to reach one-half its final value is A. directly proportional to RL. B. directly proportional to R/L. C. directly proportional to L/R. D. directly proportional to 1/(RL). E. independent of L.

C. directly proportional to L/R.

In a sinusoidal electromagnetic wave in a vacuum, the electric field has only an x-component. This component is given by Ex = Emax cos (ky + wt) The magnetic field of this wave A. has only an x-component. B. has only a y-component. C. has only a z-component. D. not enough information given to decide

C. has only a z-component.

A steady current flows through an inductor. If the current is doubled while the inductance remains constant, the amount of energy stored in the inductor A. increases by a factor of . B. increases by a factor of 2. C. increases by a factor of 4. D. increases by a factor that depends on the geometry of the inductor. E. none of the above

C. increases by a factor of 4.

A small, circular ring of wire (shown in blue) is inside a larger loop of wire that carries a current I as shown. The small ring and the larger loop both lie in the same plane. If I increases, the current that flows in the small ring A. is clockwise and caused by self-inductance. B. is counterclockwise and caused by self-inductance. C. is clockwise and caused by mutual inductance. D. is counterclockwise and caused by mutual inductance.

C. is clockwise and caused by mutual inductance.

A circular loop of wire is in a region of spatially uniform magnetic field. The magnetic field is directed into the plane of the figure. If the magnetic field magnitude is constant, A. the induced emf is clockwise. B. the induced emf is counterclockwise. C. the induced emf is zero. D. The answer depends on the strength of the field.

C. the induced emf is zero.

A coil lies flat on a tabletop in a region where the magnetic field vector points straight up. The magnetic field vanishes suddenly. When viewed from above, what is the direction of the induced current in this coil as the field fades? A) counter-clockwise then clockwise B) clockwise then counter-clockwise C) clockwise D) counter-clockwise E) There is no current induced in the coil.

D) counter-clockwise

Which one of the following lists is a correct representation of electromagnetic waves from longer wavelength to shorter wavelength? A) radio waves, infrared, microwaves, UV, visible, X-rays, gamma rays B) radio waves, UV, X-rays, microwaves, infrared, visible, gamma rays C) radio waves, microwaves, visible, X-rays, infrared, UV, gamma rays D) radio waves, microwaves, infrared, visible, UV, X-rays, gamma rays E) radio waves, infrared, X-rays, microwaves, UV, visible, gamma rays

D) radio waves, microwaves, infrared, visible, UV, X-rays, gamma rays

At a certain point in space, the electric and magnetic fields of an electromagnetic wave at a certain instant are given by E = i(6*10^3 V/m) B = k(2*10^-5T) This wave is propagating in the A. positive x-direction. B. negative x-direction. C. positive y-direction. D. negative y-direction. E. none of the above

D. negative y-direction.

In a sinusoidal electromagnetic wave in a vacuum, the electric field has only an x-component. This component is given by Ex = Emax cos (ky + wt) This wave propagates in the A. positive z-direction. B. negative z-direction. C. positive y-direction. D. negative y-direction. E. none of the above

D. negative y-direction.

An inductance L and a resistance R are connected to a source of emf as shown. When switch S1 is closed, a current begins to flow. The final value of the current is A. directly proportional to RL. B. directly proportional to R/L. C. directly proportional to L/R. D. directly proportional to 1/(RL). E. independent of L.

E. independent of L.

In a vacuum, red light has a wavelength of 700 nm and violet light has a wavelength of 400 nm. This means that in a vacuum, red light A. has higher frequency and moves faster than violet light. B. has higher frequency and moves slower than violet light. C. has lower frequency and moves faster than violet light. D. has lower frequency and moves slower than violet light. E. none of the above

E. none of the above

The rectangular loop of wire is being moved to the right at constant velocity. A constant current I flows in the long straight wire in the direction shown. The current induced in the loop is A. clockwise and proportional to I. B. counterclockwise and proportional to I. C. clockwise and proportional to I 2 . D. counterclockwise and proportional to I 2 . E. zero.

E. zero.

In one form of Tesla coil, a long solenoid with length l and cross sectional area A is closely wound with N1 turns of wire. A coil with N2 turns surrounds its center. Find the mutual inductance M.

M = 25 µH

Does the inductance of a solenoid or coil depend on the current?

No

In the series circuit shown, suppose R=300 Ω, L=60 mH, C=0.50 µF, V=50 V, and ω=10,000 rad/s. Find the reactances X_L and X_C, the impedance Z, the current amplitude I, the phase angle ϕ, and the voltage amplitude across each circuit element.

X_L = (10,000 rad/s)(60mH) = 600 Ω X_C = 1/((10,000 rad/s)(.5*10^-6)) = 200 Ω Z = sqrt((300 Ω)^2 + (600 Ω - 200 Ω)^2) = 500 Ω ϕ = tan^-1((600 Ω - 200 Ω)/300 Ω) = 53 degrees V_R = (.10 A)(300 Ω) = 30 V V_L = (.10 A)(600 Ω) = 60 V V_C = (.10 A)(200 Ω) = 20 V

Suppose the current in the outer coil is given by i2=(2 x 106 A/s)t. a) At t=3.0 µs, what is the average magnetic flux through each turn of the solenoid (coil 1) due to the current in the outer coil? b) What is the induced emf in the solenoid?

a) I_Bl = 1.5*10^-7 Wb b) emf = -50 V

The magnetic field between the poles of the electromagnet is uniform at any time, but its magnitude is increasing at a rate of 0.020 T/s. The area of the conducting loop is 120 cm2 , and the total circuit resistance, including the meter, is 5 Ω. Find the induced emf and induced current in the circuit.

emf = -A(dB/dt) = -(0.012m^2)(0.020 T/s) = -0.24 mV I = emf/R = 0.048 mA

A 500-loop circular wire coil with radius 4.00 cm is placed between the poles of a large electromagnet. The magnetic field is uniform and makes an angled of 600 with the plane of the coil; it decreases at 0.200 T/s. What are the magnitude and direction of the induced emf?

emf = -N(d(BAcosϕ)/dt) = -(500)(pi(0.04m)^2 (cos(30))(-.2T/s) = 0.435 V If you vies the coil from the left, the emf would be clockwise.

Inductor with increasing current i flowing from a to b

potential drops from a to b

Resistor with a current i flowing from a to b

potential drops from a to b

Inductor with decreasing current i flowing from a to b

potential increases from a to b