Question

1. A positive ion of charge 1 uC with a weight of 2 x 10-6 kg is released from the positive plate of a capacitor. When it reaches the negative plate, it has achieved a velocity of v = 100 m/s. Calculate the following: (6 marks total) a. What is the potential difference between the two plates? (2 marks) b. If the distance between the two plates is 1 nm and filled with vacuum, and the dimensions of the plates are 10cm by 20cm, calculate the capacitance of the capacitor. (2 marks) C. Calculate the electrical potential energy stored in the capacitor. (2 marks) 2. Two wires are running parallel with respect to each other in space from south to north, and are separated by a distance of 10 cm. They both carry currents from south to north. The wire on the left (wire 1) carries a current of 11 =10 A, and the wire on the right (wire 2) carries a current of 12 =20 A. Answer the following: (6 marks total) a. Find the direction and magnitude of the force acting on a 5-cm-long part of the wire on the left. (2 marks) b. Find the direction and magnitude of the force acting on a 10-cm long part of the wire on the right. (2 marks) c. Do these wires attract or repel each other? Why? (2 marks) 3. A 3-meter long straight wire carries a current of 30 A in a uniform magnetic fields of 0.5 T whose direction is at an angle of 45 degrees from the direction of the current. Find the magnitude of the magnetic force acting on the wire. (5 marks total) 4. Two circular wire loops are located inside the same plane, and they have a common centre. The outer loop carries a current of 20 A with a radius of 20 cm, in the clockwise direction. To create a net magnetic field of zero at their centre explain the direction and magnitude of the inner loops with a radius of 10cm. (5 marks total) 5. The single charge q1 = 3 uC is located in the space at cartesian coordinates p1 = [0,0,3). 9, is under the influence of both a point charge Q = 3 uC at location pz = [0,0,0) and a magnetic field of B = [0,0,0.5] T at P2. The velocity of q, at location P, is represented by the velocity vector v = [0,106,0 m/s. Find the sum of all forces (electrical and magnetic) acting on q, in its current location and express your answer in vector form. (8 marks total)

Answer 1

DEATILED SOLUTION ATTACHED

D 2 & E= mv Kinetic ener Potential energyzu energy=o Gain in Kinetic energy qx(V) N = Potential difference 1x2x106x(100)? 106, v (100) 2 10KV - C= to A A = (10x 200 cm 200x104m 20102 m² d = imm = -2 tox 2010 C= 10- -12 2008.85010 177 PF (6) Potential energy C Įcr² = 2x(177) % 1012 ~12 8 10 177 x 1 mJ=8.85 m 2 ar al 10cm (1) F(on Left wire) MO IZ 2T8 BIL Mo II LIZ ZT 2x107 x 1002075 S 0 2% 10% 20% soolo 20103N (b) Film Right wire) (towards 20 A wire) 3 Neolar 2FCon Left wire) = c) Attract each other

4 051 . F- IIxB 45 30A IL Band between 3 m long o= Angle I & B 2= 3m T = 304 B z 0.5 fino = sin 45 - 4 5 x 1 300 300.58 45 = 31.519N ve f = 20A 4 10 B due to a circular loop at centre Mof x 20 4 R Clockwise Bouter Mo 211 x 20 4 IT 20 MO X 2 ITX I 4IT 10 Binner = Bouter e Binner=o 20 20 + Iro 1o = -10A This I will be in Anticlock wire sense.