Question

Force between two identical metal spheres A and
B with charges as shown is F. A third identical, but
uncharged sphere C is brought in contact first with
A, then with B and finally placed at the mid-point
of the line joining A and B. The force on sphere C is
(1) F
(2) 1.5 F
(3) 1.33 F
(4) 0.75 F​

Answer 1

Answer:

Let the charge on each sphere be q then the force on each sphere is F=

r

2

kqq

=

r

2

kq

2

=2×10

−5

.....(1)

When sphere C is touched by sphere A, charge q gets equally divided between the two.

Thus, F

CA

=

r

2

/4

k(q/2)(q/2)

=

r

2

kq

2

and F

CB

=

r

2

/4

k(q/2)(q)

=

r

2

2kq

2

Net force =F

CB

−F

CA

=

r

2

2kq

2

−

r

2

kq

2

=

r

2

kq

2

=2×10

−5

N (using (1))

As F

CB

>F

CA

so net force is away sphere