Q 20 Electric Charge Force and Field 1

Q 20. Electric Charge Force and Field

1. A small object has charge Q. Charge q is removed from it and placed on a second small object. placed 1 m apart. The two objects are For the force that each object exerts on the other to be a maximum, q should be : 1. 2 Q 2. Q 3. Q/2 4. Q/4 5. 0

Q q q ( max )

2. Two identical conducting spheres A and B carry equal charge. They are separated by a distance much larger than their diameters. A third identical conducting sphere C is uncharged. Sphere C is first touched to A, then to B, and finally removed. As a result, the electrostatic force between A and B, which was originally F, becomes : 1. F/2 2. F/4 3. 3 F / 8 4. F / 16 5. 0

A, Q Spheres identical B, Q C, 0 Charges are shared equally after contact After C touching A : After C touching B : Final force between A & B :

3. Particles 1, with charge q 1, and 2, with a charge q 2, are on the x axis, with particle 1 at x = a and particle 2 at x – 2 a. For the net force on a third charged particle at the origin to be zero, q 1 and q 2 must be related by q 2 : 1. 2 q 1 2. 4 q 1 3. – 2 q 1 4. – 4 q 1 5. – q 1 / 4

2 a q q 2 a q 1

4. A particle with charge 2 C is placed at the origin. An identical particle, with the same charge, is placed 2 m from the origin on the x axis, and a third identical particle, with the same charge, is placed 2 m from the origin on the y axis. The magnitude of the force on the particle at the origin is 1. 9. 0 10– 3 N 2. 6. 4 10– 3 N 3. 1. 3 10– 2 N 4. 1. 8 10– 2 N 5. 3. 6 10– 2 N

y=2 m q = 2 C x=0 q = 2 C x=2 m q = 2 C

5. A charge Q is spread uniformly along the circumference of a circle of radius R. A point particle with charge q is placed at the center of this circle. The total force exerted on the particle q can be calculated by Coulomb's law : 1. just use R for the distance 2. just use 2 R for the distance 3. just use 2 p R for the distance 4. result of the calculation is zero 5. none of the above

Q q R f 0 by symmetry.

6. A particle with charge Q is on the y axis a distance a from the origin and a particle with charge q is on the x axis a distance d from the origin. The value of d for which the x component of the force on the second particle is the greatest is : 1. 0 2. a 3. a 2 4. a/2 5. a/ 2

Q r a f d q

7. A particle with a charge of 5 10– 6 C and a mass of 20 g moves uniformly with a speed of 7 m/s in a circular orbit around a stationary particle with a charge of 5 10– 6 C. The radius of the orbit is : 1. 0 2. 0. 23 m 3. 0. 62 m 4. 1. 6 m 5. Orbit is impossible

Q = 5 10– 6 C m = 20 g v = 7 m/s q = 5 10– 6 C R Circular motion requires a centripetal force. Coulomb force between the particles is however repulsive, and hence centrifugal.