Two tiny conducting spheres are identical and carry charges of -21.4 µC and +46.5 µC. They are separated by a distance of 2.39 cm.
(a) What is the magnitude of the force that each sphere experiences, and is the force attractive or repulsive?
(b) The spheres are brought into contact and then separated to a distance of 2.39 cm. Determine the magnitude of the force that each sphere now experiences, and state whether the force is attractive or repulsive.
Solution
here,
q1 = - 21.4 * 10^-6 C
q2 = 46.5 * 10^-6 C
r1 = 2.39 cm = 0.0239 m
a)
as the charges are of opposite sign
they will attract each other
magnitude of force , F = K * q1 * q2 /r^2
F = 9 * 10^9 * 21.4 * 10^-6 * 46.5 * 10^-6 /0.0239^2 N
F = 1.57 * 10^4 N
b)
when they are in contact
the charges are on same potential
as they are identical
the charge on each , Q = ( Q1 + Q2)/2
Q = ( - 21.4 uC + 46.5 uC) /2 = 12.55 uC
as they have the same charge
the force is repulsive
the magnitude of force , F = K * Q^2 /r^2
F = 9 * 10^9 * (12.55 * 10^-6)^2 /0.0239^2 N
F = 2.5 * 10^3 N
.
Two tiny conducting spheres are identical and carry charges of -21-4 C.docx
1. Two tiny conducting spheres are identical and carry charges of -21.4 µC and +46.5 µC. They
are separated by a distance of 2.39 cm.
(a) What is the magnitude of the force that each sphere experiences, and is the force attractive or
repulsive?
(b) The spheres are brought into contact and then separated to a distance of 2.39 cm. Determine
the magnitude of the force that each sphere now experiences, and state whether the force is
attractive or repulsive.
Solution
here,
q1 = - 21.4 * 10^-6 C
q2 = 46.5 * 10^-6 C
r1 = 2.39 cm = 0.0239 m
a)
as the charges are of opposite sign
they will attract each other
magnitude of force , F = K * q1 * q2 /r^2
F = 9 * 10^9 * 21.4 * 10^-6 * 46.5 * 10^-6 /0.0239^2 N
F = 1.57 * 10^4 N
b)
when they are in contact
2. the charges are on same potential
as they are identical
the charge on each , Q = ( Q1 + Q2)/2
Q = ( - 21.4 uC + 46.5 uC) /2 = 12.55 uC
as they have the same charge
the force is repulsive
the magnitude of force , F = K * Q^2 /r^2
F = 9 * 10^9 * (12.55 * 10^-6)^2 /0.0239^2 N
F = 2.5 * 10^3 N
