Unit 10---Electromagnetic Induction Practice Problems
Motional emf (ξ)
1. *The wingspan of a 747 airliner is 59 m. The plane is flying at a speed of 220 m/s perpendicularly through the vertical component of the earth’s magnetic field (5 E –6 T). Find the emf induced across the wings of the plane. (0.065 V)
2. *Suppose, in the picture to the right, you are moving the rod to the right at a speed of 5 m/s in a direction perpendicular to an 0.80 T magnetic field. The rod has a length of 1.6 m and a negligible resistance. The rails (wires) also have a negligible resistance. Picture a light bulb (R = 96 ohm) as being in the circuit at the far left. Find
a. The emf produced by the rod. (6.4 V)
b. The induced current in the circuit. (0.067 A)
c. The electrical power delivered to the bulb. (0.43 W)
d. The energy used by the bulb in 60 seconds. (25.6 J)
e. For the above problem, the rod experiences a magnetic force due the current moving through it and the magnetic field it is in. Calculate the size of the force acting on the rod in the magnetic field. (0.086 N)
f. For the above problem, how much work would you have to do to keep the rod moving at a constant 5 m/s for 60 seconds? (~26 J)
3. *Suppose the light bulb in the previous problem was replaced with a short wire of zero resistance and the resistance of the rails is negligible. The only resistance in the circuit is from the moving rod, which is iron and has a resistivity of 9.7 E –8 ohm-meter. The rod has a cross-sectional area of 3.1 E –6 m2 and moves with a speed of 2 m/s. The magnetic field has an intensity of 0.05 T. What is the induced current in the rod? (3.2 A)
4. *The horizontal component of the earth’s magnetic field at a certain location is 2.6 E-5 T and points due North.
a. What motional emf appears in the 0.80 m vertical radio antennae of a car traveling east with a speed of 27 m/s? (5.62 E-4 V)
b. What motional emf appears if the car is traveling north or south? (0 V)
5. *Near San Francisco, where the vertically downward (toward the surface of the earth) component of the earth’s magnetic field is 4.8 E-5 T, a car is traveling forward at 25 m/s perpendicularly to the magnetic field. An emf of 2.4 E –3 V is induced between the sides of the car.
a. Which side of the car (the driver’s or the passenger’s) is positive? The driver’s side.
b. What is the width of the car? 2m
Magnetic Flux
6. *A hand is held flat and placed in a uniform 0.35 T magnetic field. The hand has an area of 0.0160 m2 and negligible thickness. Determine the magnetic flux that passes through the hand when the normal (a line that is perpendicular to the hand’s surface) to the hand is
a. Parallel to the magnetic field. (0.0056 Wb)
b. Perpendicular to the magnetic field. (0 Wb)
7. A rectangular coil of wire is situated in a constant 0.5 T magnetic field. The coil has an area of 2 m2. Determine the magnetic flux for the following angles: 0, 60, and 90 degrees. (1 Wb, 0.5 Wb, 0 Wb)
8. A house has a floor area of 112 m2 and an outside wall that has an area of 28 m2. The earth’s magnetic field here has a horizontal component of 2.6 E-5 T that points due north and a vertical component of 4.2 E-5 T that points straight down toward the earth. Determine the magnetic flux through the wall if the wall faces
a. North. (7.28 E –4 Wb)
b. East. (0 Wb)
c. Calculate the magnetic flux that passes through the floor. (4.70 E-3 Wb)
Changing Magnetic Flux (Faraday’s Law—determining the induce emf )
9. *A coil of wire consists of 20 turns, each of which has an area of 1.5 E-3 m2. A magnetic field is perpendicular to the surface of each loop at all times. At t= 0s, the magnitude of the magnetic field at the location of the coil is 0.05 T. At t = 0.10 second later, the magnitude of the field at the coil has increased to 0.060 T.
a. Find the average emf induced in the coil during this time. (-3 E –3 V)
b. What would be the value of the average emf if the magnitude of the magnetic field decreased from 0.06 T to 0.050 T in 0.10 seconds? (3 E-3 V; same potential difference, just opposite polarity)
10. *A flat coil of wire has an area of 0.020 m2 and consists of 50 turns. The coil is initially oriented so its opening is perpendicular to a magnetic field of 0.18T. The coil is then rotated through an angle of 30 degrees in 0.10 seconds.
a. Determine the average induced emf. (+0.24 V; positive simple due to the polarity being in a certain direction)
b. What would the induced emf be if the coil were returned to its initial orientation? (-0.24 V; negative simply due to the polarity being opposite from the previous polarity)
11. A 300 turn rectangular loop of wire has an area of 5 E –3 m2. A magnetic field is suddenly turned on and 0.8 seconds later its value increases to 0.4 T. The field is directed at an angle of 30 degrees with respect to the normal of the loop.
a. Find the average induced emf in the loop. (-0.65 V)
b. If the loop is a closed circuit whose resistance is 6 ohms, determine the average induced current. (0.11 A)
12. A straight wire is bent into a single loop in the form of a circle with a radius of 2 cm. A constant magnetic field of 0.55 T is directed perpendicular to the plane of the loop. Someone grabs the ends of the wire and pulls so the radius of the circle shrinks to zero in 0.25 s. What is the average emf induced between the ends of the wires? (2.76 E-3 V)
13. A 1.5 m long aluminum rod is rotating about an axis that is perpendicular to one end. A 0.16 T magnetic field is directed parallel to the axis (so the rod perpendicularly slices through the field). The rod rotates through ¼ of a circle in 0.66 s. What is the magnitude of the average induced emf generated between the ends of the rod during this time? (0.43 V)
14. A piece of copper wire is formed into a single circular loop of radius 12 cm. A magnetic field is oriented parallel to the normal to the loop and increases from 0T to 0.60 T in a time of 0.45 s. The wire has a resistance per unit length of 3.3 E –2 ohm/meter. What is the average electrical energy dissipated in the wire in this amount of time? (6.6 E-2 J)
Both Faraday’s and Lenz’s Laws (determining the polarity of the induced emf)
15. *In the diagram to the right, what is
a. the direction of the bar magnet’s magnetic field inside the coil? (toward the magnet or into the page as the diagram is drawn)
b. the direction of the flux change (is it increasing or decreasing in the coil)? (increasing)
c. the direction of the induced magnetic field inside the coil? (opposite the direction of the bar magnet’s field or out of the page as the diagram is drawn)
d. The direction of the induced conventional current in the loop of wire? (counterclockwise as the diagram is drawn)
e. The polarity of the emf of the loop of wire? (the lower left of the loop is positive and the lower right of the loop is negative) (picture the current moving through the circuit and picture the loop as a battery and think about which end of the loop/battery needs the be a positive polarity in order for the conventional current to flow through the circuit in the way it does)
16. Repeat the above problem if the bar magnet was now moving away from the loop of wire.
a. Still toward the magnet or into the page
b. Decreasing
c. The same direction as the bar magnet’s field (into the page)
d. Clockwise
e. Lower left is negative and lower right is positive
17. Repeat the above problem if the N-pole was facing the loop of wire and moving toward the loop of wire.
a. Away from the bar magnet or out of the page
b. Increasing
c. Into the page; opposite the bar magnet’s field
d. Clockwise
e. Lower right is positive and lower left is negative
18. Repeat the above problem if the N-pole was facing the loop of wire but moving away from the loop of wire.
a. Away from the bar magnet or out of the page
b. Decreasing
c. Out of the page; in the same direction as the bar magnet
d. Counterclockwise
e. Lower left is positive and lower right is negative
19. A metal hoop is suspended from a support by a string and a magnet is moved horizontally back and forth through the hoop. What is the direction of the induced conventional current in the hoop if the magnet is moved
a. N-pole facing the hoop and moving toward the hoop? (counterclockwise)
b. N-pole facing the hoop and moving away from the hoop? (clockwise)
c. S-pole facing the hoop and moving toward the hoop? (clockwise)
d. S-pole facing the hoop and moving away from the hoop? (counterclockwise)
20. * The diagram to the right is of a constant magnetic field in a region of space. The field is directed perpendicularly into the plane of the paper. Outside the region there is no magnetic field. A copper ring slides through the region from left to right across the paper. For each of the five positions (from left ring to right ring), determine if an induced conventional current exists in the ring and, if so, in what direction.
Ring 1à no induced current
Ring 2 à counterclockwise
Ring 3 à no induced current (flux isn’t changing)
Ring 4 à clockwise
Ring 5 à no induced current
21. *In the diagram to the right, determine:
a. The direction of the current inside the rod. (positive charges to the top, negative charges to the bottom)
b. The polarity of the induced emf in the rod. (the top of the rod is positive and the bottom of the rod is negative)
c. The direction of the induced current in the circuit. (counterclockwise)
d. The direction of the induced magnetic field around the rod but inside the loop of wire.
i. Using a RHR (out of the page)
ii. Using Lenz’s Law (since flux is into the page and increasing in that region, the induced magnetic field must be opposite the existing field to counter it therefore the induced field must be out of the page)
e. The direction of the magnetic force on the rod due to the original magnetic field and the motion of the current in the rod. (to the left, opposite the rod’s velocity)
22. A 2 kg rod is suspended horizontally across two vertically oriented rails that are part of a circuit (see previous problem’s picture but think of it rotated ¼ turn to the left so the rod is at the top of the diagram). The length of the rod that is in the field is 1.25m. A magnetic field of 1.8 T surrounds the circuit and is directed into the page. The rod is released and begins to slide vertically down with constant velocity generating an emf across the ends of the wire. What is the magnitude and direction of the induced current? (8.71 A, clockwise)
2
Unit 10 AP Practice Problems Electromagnetic Induction