Two 1. charged particles, Q1 = 6 C with mass 2 g and Q2 = 3 C with mass 1 g, are placed at points A and B which are 8 cm apart. (a) If Q1 is released from rest at point A, calculate: (i) The acceleration of Q1 as it is being released. (ii) The speed of Q1 after a very long time. (b) If both charges are released simultaneously from rest at points A and B, calculate the speed of Q1 after a very long time.
Q1
8 cm
2. Two equal charges, each of 8 C, are 8 m apart. Point A is 3 m below the midpoint of the two charges. a) What is the potential at point A?
Q2 8 C 3m 8 C
b) What is the electric field at point A? c) A particle of mass 5 g and charge 2 nC is released from rest at point A. What is its initial acceleration? d) What will be the speed of this particle After traveling a distance of 3 m?
A
3. Consider the circuit shown: a) Req = ? b) Current in 15 resistor? c) Power dissipated in the 40 resistor? d) If the battery is rated at 20 A.h., how long will it last?
40 40 V 20 8 15
4. Consider the circuit shown. (a) The capacitor is fully charged. (i) Calculate the currents in all resistors. (ii) What is the charge on the capacitor? (b) After fully charging the capacitor, the switch S is now opened. After how long from the moment the switch is opened will the charge on the capacitor be equal to of its initial value?
5. Two long parallel wires are 1 cm apart. The B-field at point P is 3.510-5 T and points out of the plane of the wires. (a) What is I2? (b) Where in the plane of the two wires will the B-field be zero?
I1
1 cm
6. A single loop of radius 6 cm is formed in the middle of a long, thin, insulated wire carrying a current of 4 cm. What is the B-field at the centre of the loop?
I2
3 cm
Bout= 3.510-5 T
1
7. Two long parallel wires, 16 cm apart, carry currents of 10 A and 15 A as shown. Point P is 8 cm above the midpoint of the line joining the two currents. a) Where does the B-field vanish? b) Calculate the B-field at point P.
I2 = 15 A
16 cm
8. An ion with charge of +e enters the region of uniform B-field with a velocity of 5 106 m/s. The path of the particle is shown in the diagram. a) What is the direction of the B-field? b) What is the magnetic force acting on the particle at point A? c) What is the mass of the particle?
v
18 cm
P
A
I1 = 10 A
B-field region, B = 5.2 10-3 T
9. A singly ionized potassium atom (charge = 1.6 10-19 C, mass = 6.49 10-26 kg) is moving a with speed of 2.5 103 m/s in a uniform perpendicular B-field as shown. B = 1.2 T a) Determine the magnitude of the magnetic force on the K ion. b) Determine the radius of the K's path. c) Is the ion's motion clockwise or counterclockwise?
Path of K ion
into
10. A 4 cm 3 cm rectangular loop is made of a 0.25 mm radius Al wire. The resistivity of Al is 2.6510-8 m. The loop is placed in a region of a uniform Bfield which extends indefinitely to the right and to the left. (a) What is the resistance of the loop? (b) The B-field starts to increase at a uniform rate of 0.1 T/s. Determine the induced current in the loop? (c) If the B-field is kept constant at 5 T, and the loop is moving to the right at a constant speed of 3.5 cm/s, will there be an induced current in the loop? If so, calculate its value.
3 cm
4 cm
11. A conducting circular loop is near a straight wire carrying a current I. Determine the direction of the induced current in the loop for the following cases: a) The loop moves horizontally to the right with constant speed. b) The loop moves vertically up with constant speed. c) The current in the straight wire increases uniformly with time.
I
12. Consider the following ac circuit: Current leads the voltage by 24 degrees. What are the two elements? What is the impedance? What is the power dissipated in the circuit?
73 V(rms) 60 Hz
~
I(rms) = 8.3 A
2
13. The average power dissipation in the ac circuit shown is 12 W. a) Calculate the impedance of the circuit. b) What is the peak value of the ac voltage source? c) What is the phase angle between current and voltage? Which is leading? d) If one can vary the frequency of the source, what would be the highest average power dissipation that can be achieved in this circuit?
C = 2 F
14. In the AC circuit shown, the potential difference across the capacitor and the resistor, VAC, is 24 Vrms. Similarly, the potential difference across the inductor and the resistor, VDB, is 24 Vrms. C = 40 F (a) What is the frequency of the source? (b) What is the rms value of the source? (c) What is the power dissipated in this circuit?
A D C
~
L = 0.08 H
R = 40
B
180 Hz
~
L = 0.2 H
R = 300
15. In the circuit shown, the current, in ampere's, is given by: I = 2.55 sin(250 t ) The rms value of the voltage across R, L, and C are all equal to 11 V.
C
a) What is f? b) What is R? c) What is L? d) What is C? e) What is Vrms?
L
Vrms, f
~
R
3