How many excess electrons must be distributed uniformly within the volume of an

Question

How many excess electrons must be distributed uniformly within the volume of an isolated plastic sphere 21.0 cm in diameter to produce an electric field of 1350 N/C just outside the surface of the sphere? What is the electric field at a point 15.0 cm outside the surface of the sphere?

An insulating hollow sphere has inner radius a and outer radius b. Within the insulating material the volume charge density is given by (r)=r,where is a positive constant.

What is the magnitude of the electric field at a distance r from the center of the shell, where a<r<b

A point charge q is placed at the center of the hollow space, at r=0. What value must qhave (sign and magnitude) in order for the electric field to be constant in the region a<r<b?

What then is the value of the constant field in this region?

Explanation / Answer

1)

Gauss Law: EA = Q/ ======> Q = EA
Sphere surface area: A = 4r²: ======> Q = E4r² = Er²/k
(Calculate either with = 8.85×10 ¹² F/m or k = 8.99×10 Nm²/C²)
=> Q = 1350N/C*(0.105m)² / 8.99×10Nm²/C² = 1.66×10 C

(1.66×10 C) / (1.6×10 ¹C/electron) = 1.0375×10¹º = 10.4 billion electrons in excess.

E = kQ/r^2 = (8.99*10^9*1.66*10^-9)/(0.255)^2 = 229.5 N/C

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