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Electromagnetism Problem Set

Which equations do I use for what?

Force on a moving charged particle: F = qvBsinθ

Force on a current-carrying wire: F=BILsinθ

Magnetic field in a solenoid:

Flux (magnetic field passing through an area):

Induced voltage in a coil of wire (Faraday's Law):

Motional EMF (induced voltage in a conductive bar): ε=Blv

Back EMF in a motor: ε(back) = V-IR

Transformers:

Regular Electromagnetism Problems:

1. The magnetic field at the centre of a solenoid of length 0.25 m is 1.2 102 T. The current in the windings is 8.5 A.a) How many windings does the solenoid have? b) If the cross-sectional area of the solenoid is 8.5 104 m2, what is the flux through it?

2. A solenoid has a length of 0.20 m, a diameter of 0.030 m and 500 windings. The magnetic field at its centre is 0.035 T. What is the current in the windings?

3. An aircraft whose wingspan is 35 m carries a static charge of 0.60 C. It travels at 240 m/s perpendicular to a 2.5 104 T magnetic field. a) What magnetic force does the aircraft experience?b) What is the emf induced across the wings of the aircraft?

B=μ0NIl

Φ=BA¿

ε=−N ΔΦΔt

N p

N s=V pV s

=I sI p

4. A proton moves with a speed of 5.6 105 m/s at right angles to a uniform 4.0 105 T magnetic field. a) What is the radius of curvature for the motion of the proton?b) Describe the path of the proton in the magnetic field and use principles of physics to explain the proton’s motion.

5. Find the radius of curvature of the path of an electron first accelerated through a potential difference of 150 V and then passing through a perpendicular magnetic field of 3.5x10-3 Tesla.

6. A coil having 150 turns and a cross-sectional area of 0.032 m2 is oriented with its plane perpendicular to a 0.12 T magnetic field. If the field increases to 0.46 T in 0.25 s, what emf is induced in the coil?

7. A bar magnet is moving toward a solenoid as shown.What is the direction of the current through G and what is the direction of the magnetic field produced by this current at location P inside the solenoid?

8. A circular coil having 130 turns, a radius of 3.7 cm, and a resistance of 2.6 sits flat on the ground in a vertically upward magnetic field of 3.0x10-3 T. Find the magnitude and direction (as seen from above: either clockwise or counterclockwise) of the induced current in the coil if:a) the magnetic field is reduced to zero in 1.5 seconds.b) the coil is rotated 90 degrees in 3.8 seconds so that it ends up with its plane parallel to the field.c) the field is reversed in direction and doubled in 2.9 seconds.

9. A transformer has 740 primary and 66 secondary windings. The primary coil is connected to a 110 V AC power supply that delivers a 0.30 A current to the transformer.a) Find the secondary voltage. b) Find the secondary current.

10. A charged particle is accelerated through a potential difference of 75 V and then enters a region of uniform magnetic field of strength 6.8x10-3 T, which is perpendicular to the direction of the particle’s velocity. If the radius of the circular path is 13 cm, find the speed of the particle.

Pride Point Challenge Problems:

1. The diagram below shows a 0.010 kg metal rod resting on two long horizontal frictionless rails which remain 0.40 m apart. The circuit has a resistance of 2.5 and is located in a uniform magnetic field of 0.20 T. Find the initial acceleration and maximum velocity for the rod.

2. A rectangular conducting loop of mass 45 g and resistance 1.5 Ω is dropped in the direction shown through a uniform magnetic field of 1.8 T oriented parallel to the ground. Find the maximum speed that the loop will reach.

Answers to Regular Electromagnetism Problems:1. 281, 1.0x10-5 Wb2. 11 A3. 0.036 N, 2.1 V4. 145 m5. 0.012 m6. 6.5 V7. x y, right8. a) 0.43 mAb) 0.17 mAc) 0.67 mA9. 9.8 V, 3.4 A10. 1.7x105 m/s

Answers to Pride Point Challenge Problems:1. 188 m/s, 48 m/s2

2. 0.14 m/s