Answer:
0.782m
Explanation:
Parameters given:
Volume charge density, ρ = 10 * 10^(-9) C/m³
Electric field outside the shell, E = 120 N/C
Outer radius, R2 = 1.1m
Inner radius, R1 =?
Volume charge density, ρ is given as:
ρ = Q/V
V = volume of shell = 4/3 * π * (R2 - R1)³
Therefore,
ρ = Q/[4/3 * π * (R2 - R1)³] _______(1)
The electric field outside the shell is given as:
E = kQ/(R2 - R1)² ________(2)
We can make charge, Q, the subject of the formula:
From (1):
Q = 4ρ/3 * π * (R2 - R1)³
From (2):
Q = E/k * (R2 - R1)²
Equating both formulae:
4ρ/3 * π * (R2 - R1)³ = E/k * (R2 - R1)²
=> (R2 - R1)³/(R2 - R1)² = 3E/(4πρk)
(R2 - R1) = 3E/(4πρk)
=> R1 = R2 - 3E/(4πρk)
Inserting the values of all parameters, k = Coulumbs constant:
R1 = 1.1 - (3 * 120)/(4 * π * 10 * 10^(-9) * 9 * 10^9)
R1 = 1.1 - 360/1131.12
R1 = 1.1 - 0.318
R1 = 0.782m
