Question

Two identical metal balls of radii 2.50

cm are at a center to center distance of
1.00 m from each other. Each ball is
charged so that a point at the surface of
the first ball has an electric potential of
+1.20 x 103 V and a point at the surface
of the other ball has an electric
potential of -1.20 x 103 V. What is the total charge on each ball?

Answer 1

+1.33 ×
`10^(-7)` C and -1.33 ×
`10^(-7)` C respectively.

Step-by-step explanation:

Electric potential (V) is the work done in moving a unit positive charge from infinity to a reference point within an electric field. It is measured in volts.

V =
`(kq)/(r)` ............. 1

where: k is a constant = 9 ×
`10^(9)` N
`m^(2) C^(-2)`, q is the charge and r is the distance between the charges.

From equation 1,

q =
`(Vr)/(k)` ............... 2

The charge on each ball can be determined as;

given that; V = 1.2 ×
`10^(3)`, k = 9 ×
`10^(9)` N
`m^(2) C^(-2)` and r = 1.00 m.

From equation 2,

q =
`(1.2*10^(3) * 1.0)/(9*10^(9) )`

= 1.33 ×
`10^(-7)` C

Thus, the charge on the first ball is +1.33 ×
`10^(-7)` C, while the charge on the second ball is -1.33 ×
`10^(-7)` C.