212 - Problem Set 6

Physics 212 Spring 2009 Problem Set #6

1)Consider a series RC circuit at the left where C = 6 µF, R = 2 MΩ, and ε = 20 V. You close the switch at t = 0. Find (a) the time constant for the circuit, (b) the half-life of the circuit, (c) the current at t = 0, (d) the voltage across the capacitor at t = 0, and (e) the voltage across the resistor after a very long time.

ε C

2)Given the circuit at the right in which the following values are used: R1 = 5 kΩ, R2 = 10 kΩ, C = 8 µF, and ε = 20 V. You close the switch at t = 0. Find (a) the current through R2 at t=0, and (b) the voltage across R1 after a long time.

ε

R1

A 0.5 m length of wire is bent to form a single square loop. The loop has 12 A of current running through it. The loop is placed in a magnetic field of 0.12 T as shown at the right (side view of loop). What is the maximum torque that the loop can experience?

F

8) Two very long wires, as shown in the diagram at the right, each carry currents of 8.0 A, however, they flow in opposite directions. The distance between the two wires is 0.12 m. Calculate the net magnetic field at point A, which is 0.03 m to the left of the left wire, and at point B, which is halfway between the two wires.

C

3)Given the circuit at the right in which the following values are used: R1 = 20 kΩ, R2 = 12 kΩ, C = 10 µF, and ε = 25 V. You close the switch at t = 0. Find (a) the current in R1 and R2 at t=0, (b) the voltage across R1 after a long time. (Careful with this one.)

7)

R

R2

B

F

A

B

R1 ε

C

R2

9) A mass spectrometer is shown below. A single charged ion is shot through the velocity selector into the rectangular deflection chamber. The electric field between the plates of the velocity selector is 950 V/m. The magnetic field in the velocity selector and the deflection chamber is 0.93 T. Calculate the radius of the path of the singly charged ion that has a mass 2.18 x 10-26 kg. 8)

4)

v v Using the drawings below: (a) Find the direction of the force B B on a proton moving through the magnetic field. (b) Repeat9) v v with an Belectron. B (a)

(b)

(c)

Electric Field

(d)

5)An alpha particle has a charge of +2e and a mass of 6.64 x 10-27 kg. It is accelerated from rest through a potential difference of 1.2 x 106 V and then enters a uniform magnetic field whose strength is 2.2 T. The alpha particle moves perpendicular to the field. Calculate (a) the speed of the alpha particle, (b) the magnitude of the magnetic force exerted on it, and (c) the radius of its circular path. 6)

Velocity Selector

A 50 g horizontal copper rod has a length of 1.0 m. Calculate the minimum current in the rod so that it will float in a horizontal magnetic field of 2.0 T.

B

10)An electron moves at a speed of 1.0 x 10

m/s in a circular path of radius 2 cm inside a solenoid. The magnetic field of the solenoid is perpendicular to the plane of the electron’s path. Calculate (a) the strength of the magnetic field inside the solenoid and (b) the current in the solenoid if it has 25 turns per centimeter.

ANSWERS: 1) a) 12 s, b) 8.32 s, c) 1 x 10-5 A

4

5) a) 1.08 x 107 m/s 9) 1.49 x 10-4 m b) 7.6 x 10-12 N 10) a) 2.8 x 10-6 T

2) a) 2 mA, b) 20 V

c) 1.02 x 10-1 m

3)a) I =1.25 mA, I =0 6) 0.245 A 1

2

b) 15.6 V 4) a) P-West, E-East

7) 0.023 Nm 8) a) 4.3 x 10-5 T b) 5.3 x 10-5 T

b) 0.89 mA