- #1
Minhtran1092
- 28
- 2
Homework Statement
A metal sphere with radius r_a is supported on an insulating stand at the center of a hollow, metal spherical shell with radius r_b. There is charge +q on the inner sphere and charge -q on the outer spherical shell. Take the potential V to be zero when the distance r from the center of the spheres is infinite.
What is the equation V(r) that models the potential in the region r_a < r < r_b?
Homework Equations
ΔV = -∫E(r)∂r
ψ=Q/ε_0
E∫A = ψ; ∫A = 4πr^2
The Attempt at a Solution
1. V(∞) - V(r) = ∫E(r)∂r (from ∞ to r) = ∫E(r)∂r (from ∞ to r_b) + ∫E(r)∂r (from r_b to r);
2. ∫E(r)∂r (from ∞ to r_b) should evaluate to a constant since E(r) = 0 by Gauss' Law (Taking the Gaussian object to have r > r_b, the enclosed charge is -q + q = 0; Electric flux = 0 and therefore electrical field outside the r_b shell is 0.)
3. ∫E(r)∂r (from ∞ to r) = Constant + ∫E(r)∂r (from r_b to r)
4. ∫E(r)∂r (from r_b to r) evaluates to q/(ε_0*4*π)| (from r_b to r)
V(r_a< r < r_b) = q/(ε_0*4*π)| (from r_b to r) is as far as I got.
Did I make a wrong assumption?