Question

Two small plastic spheres are given positive electrical charges. When they are 20.0 cm apart, the repulsive force between them has magnitude 0.200 N.

1. What is the charge on each sphere if the two charges are equal? (C)


2. What is the charge on each sphere if one sphere has four times the charge of the other? (C)

Answer 1

1) +9.4 x 10^-7 C

2) +4.72 x 10^-7 C and +1.9 x 10^-6 C

Step-by-step explanation:

The two positive charges will repel each other

Repulsive force on charges = 0.200 N

distance apart = 20.0 cm = 0.2 m

charge on each sphere = ?

Electrical force on charged spheres at a distance is given as

F =
`(kQq)/(r^(2) )`

where F is the force on the spheres

k is the Coulomb's constant = 8.98 x 10^9 kg⋅m³⋅s⁻²⋅C⁻²

Q is the charge on of the spheres

q is the charge on the other sphere

r is their distance apart

since the charges are equal, i.e Q = q, the equation becomes

F =
`(kQ^(2) )/(r^(2) )`

making Q the subject of the formula

==> Q =
`\sqrt{(Fr^(2) )/(k) }`

imputing values into the equation, we have

Q =
`\sqrt{(0.2*0.2^(2) )/(8.98*10^(9) ) }` = +9.4 x 10^-7 C

If one charge has four times the charge on the other, then

charge on one sphere = q

charge on the other sphere = 4q

product of both charges =
`4q^(2)`

we then have

F =
`(4kq^(2) )/(r^(2) )`

making q the subject of the formula

==> q =
`\sqrt{(Fr^(2) )/(4k) }`

imputing values into the equation, we have

q =
`\sqrt{(0.2*0.2^(2) )/(4*8.98*10^(9) ) }` = +4.72 x 10^-7 C

charge on other sphere = 4q = 4 x 4.72 x 10^-7 = +1.9 x 10^-6 C

Answer 2

A. 2.97x 10^-6C

B. 1.48x10^ -6 C

Step-by-step explanation:

Pls see attached file