A total charge of Q = 3.5·10 –6 C is placed on a conducting sphere (sphere 1) of

Question

A total charge of Q = 3.5·10–6 C is placed on a conducting sphere (sphere 1) of radius R = 44.7 cm.

a) What is the electric potential, V1, at the surface of sphere 1 assuming that the potential infinitely far away from it is zero? (Hint: What is the change in potential if a charge is brought from infinitely far away, where V() = 0, to the surface of the sphere?)

b) A second conducting sphere (sphere 2) of radius r = 8.7 cm with an initial net charge of zero (q = 0) is connected to sphere 1 using a long thin metal wire. How much charge flows from sphere 1 to sphere 2 to bring them into equilibrium?

c) After the spheres are connected, what is the absolute value of the electric field on the surface of sphere 1?

d) After the spheres are connected, what is the absolute value of the electric field on the surface of sphere 2?

Explanation / Answer

Q = 3.5·10–6 C
(a)
Electric Potenital at the surface of a sphere = k*q/r
Where r is the distance from the center to the surface = radius of Sphere.
V = (8.9*10^9 * 3.5*10^-6) / (44.7*10^-2)
V = 6.96 *10^4 Volt

(b)
Let the Final Charge in two sphere be Q1 & Q2 in Sphere 1 & 2 respectively.
Q1 = Q* r1/(r1+r2)
Q1 = 3.5*10^-6 * 44.7 / (44.7 + 8.7) C
Q1 = 2.93 * 10^-6 C

A Charge is conserved,
Q2 = (3.5 - 2.93) * 10^-6 C
Q2 = 0.57 *10^-6 C

Charge flows from sphere 1 to 2 , = 0.57 *10^-6 C

(c)
Electric Field at the surface of a sphere = k*q/r^2
Due to Q1 , E1 = (8.9*10^9 * 2.93*10^-6) / (44.7*10^-2)^2
E1 = 1.31 * 10^5 N/C

(d)
Electric Field at the surface of a sphere = k*q/r^2
Due to Q2 , E2 = (8.9*10^9 * 0.57*10^-6) / (8.7*10^-2)^2
E2 = 6.7 * 10^5 N/C

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.