Question

Magnetism

1. (4) An unknown particle travelling at a velocity of 2.20x10⁶ m/s to the right as seen by an observer, enters a region that has an electric field of magnitude 750 V/m pointed away from the observer. Ignore gravity for this question.

(a) What is the direction and magnitude of the perpendicular magnetic field which would best cancel out the effect of the electric field so that the particle passes through undeflected?

(b) If while travelling 0.200 m, with only the magnetic field on, the particle is deflected by 0.22 mm, what is the charge to mass ratio of the particle?

2. (4) Consider a long straight wire that carries a current of I₁= 375 mA upward.

(a) What is the magnitude and direction of the magnetic field generated by the wire a distance of 1.00 cm to the left of the wire?

(b) Now consider that another long straight wire is placed in parallel with the first one, at the location considered in a, 1.00 cm to the left of the first wire. This new wire has a current of I₂= 236.0 mA downward. What is the magnitude and direction of force per length of wire from the first wire on the second?

(c) Generalize your findings from b to make a statement about in which cases wires carrying current are attracted to, or repelled from, one another

Faraday’s Law

3. (4) A 75 turn rectangular coil of height 5.40 cm and width 3.40 cm rotates about a perpendicular axis in a uniform magnetic field of 825 mT. The maximum emf induced in the coil is 6.25 V.

(a) Find the maximum magnetic flux through the coil.

(b) Find the coil’s angular velocity in revolutions per minute.

(c) Sketch the magnetic flux through the coil, and the induced emf, as a function of time.

Inductance

4. (4) Consider an air-core solenoid with a circular cross-section, radius 8.00 mm and length 20.00 cm, and exactly 350 windings. If a current of 4.75 mA is sent through the solenoid

(a) If the current is going through the coils clockwise as seen from above the coils, sketch the magnetic field that is generated

(b) Determine the magnitude of the average magnetic field inside the solenoid

(c) Determine the inductance of the solenoid

5. (4) Consider an RL circuit that can initially be thought of as containing an ideal battery of voltage 2.10 V, an ideal resistor of resistance 910 Ω and an ideal inductor of inductance 77.50 mH.

(a) Another ideal inductor, of inductance 125.0 mH, is added in series. Find the new equivalent inductance and the new time constant for the circuit.

(b) The circuit is closed at t=0. Sketch the behaviour of the voltage across the resistor and the voltage across the inductor as a function of time

(c) Find the current in the circuit at time t=3.00 μs.

Answer 1

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