Question

A spherical capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has a radius of ra = 12.3 cm , and the outer sphere has a radius of rb = 15.1 cm . A potential difference of 120 V is applied to the capacitor.
(a) What is the capacitance of the capacitor?
(b) What is the magnitude E1 of the electric field E? at radius r= 12.8cm, just outside the inner sphere?
(c) What is the magnitude of E? at r= 14.7cm, just inside the outer sphere?

Answer 1

Answer: a) 73.41 10^-12 F; b)4.83* 10^3 N/C; c) 3.66 *10^3 N/C

Explanation: To solve this problem we have to consider the following: The Capacity= Charge/Potential Difference

As we know the capacity is  value that depend on the geometry of the capacitor, in our case two concentric spheres.

So Potential Difference between the spheres is given by:

ΔV=-$\int\limits^a_b {E} \, dx$

Where E = k*Q/ r^2

so we have $\int\limits^a_b {K+Q1/r} \, dr$

then

Vb-Va=k*Q(1/b-1/a)=kQ (ab/b-a)

Finally using C=Q/ΔV=ab/(k(b-a))

To caclulate the electric firld we first obtain the charge

Q=ΔV*C=120 V*73.41 10^-12 F=8.8 10^-9 C

so E=KQ/r^2 for both values of r

r=12.8 cm ( in meters)

r2=14.7 cm

E(r1)=4.83* 10^3 N/C

E(r2)=3.66 *10^3 N/C