I need help with thise problem. I will rate, I promise. a). Find from the first
ID: 2105567 • Letter: I
Question
I need help with thise problem. I will rate, I promise.
a). Find from the first principle, the potential of a hollow sphere. Then find the potential difference between two concentric spheres, one with a radius ("a") within a sphere of radius ("b").
b). Find the capacitance of the sphere
c). Find the capacitance of an isolated sphere. Make the radius of the outer sphere really big.
d). If earth's surface field is about 150 N/C, find the capacitance of the earth. Treat earth as an isolated capacitor. Find the total charge on earth's surface.
Explanation / Answer
a) Suppose a charge of Q is deposited slowly on an uncharged sphere of radius r. By 1st principle potential of a point is work done per unit +tive charge in bringing it to that point from infinity. Electric field at x>r , E = KQ/x^2 F= q.E dW = q.E.dx integrate this x from infinity to r. By 1st principle , potential of a sphere with charge Q, V= W/q = -kQ/r Using abhove relation potential difference between 2 spheres = V1- V2 =(kQ/a) - (kQ/b) = KQ(1/a -1/b) b.) For capacitor; Q= CV So, capacitance C = Q/V for two spheres,C= ab/K(a-b) C.) If a>>b , a-b cab be writen as a. Capacitance of an isolated sphere of radius b = ab/k.a = b/k D.) Surface field for sphere = KQ/ r^2 = 150 N/C for earth by putting value of K and radius of earth,r get Q. Hope, my help will be helpful to u...