Q20. 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. The two objects are

placed 1 m apart. 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

2

q Q qf k

r

22 0

d f kQ q

d q r

2

Qq

2

2 22 0

d f k

d q r ( max )

Q q q

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. 3F / 8

4. F / 16

5. 0

2A C

QQ Q

Spheres identical Charges are shared equally after contact

After C touching A :

1 3

2 2 4B C

QQ Q Q Q

After C touching B :

2

3 3

2 4 8

k Q QF F

r Final force between A & B :

A, Q B, Q C, 0

3. Particles 1, with charge q1, and 2, with a charge q2, are on

the x axis, with particle 1 at x = a and particle 2 at x –2a.

For the net force on a third charged particle at the origin to

be zero, q1 and q2 must be related by q2 :

1. 2 q1

2. 4 q1

3. – 2

q1

4. – 4

q1

5. – q1 /

4

1 2

3 220

2

q qk q

a a

2 14q q

q1q2

q2a a

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

29 6

22

9 10 2 102 1.27 10

2N

x = 0q = 2C

x = 2 mq = 2C

y = 2 mq = 2C

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 2R for the distance

3. just use 2R for the distance

4. result of the calculation is zero

5. none of the above

f 0 by symmetry.

Q

Rq

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

3/22 2 2

1 d df k q Q k q Q

r r a d

3/2 5/22 2 2 2

21 30

2

d dd fk q Q

d d a d a d

2

ad

Q

a

qd

f

r

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

Circular motion requires a centripetal force.

Coulomb force between the particles is however repulsive, and hence centrifugal.

Q = 5 10–6 Cm = 20 gv = 7 m/s

R

q = 5 10–6 C