A hollow metal sphere has inner radius R1=20cm and outer radius R2 = 50cm and ha

Question

A hollow metal sphere has inner radius R1=20cm and outer radius R2 = 50cm and has a charge of +2.0uC (MicroCoulombs);

1) What is the strength of the electric field at the center of the sphere?
2) What is the strength of the electric field 10cm from the center of the sphere?
3) What is the strength of the electric field 30cm from the center of the sphere?
4) What is the maximum strength of the electric field caused by the sphere? Where is it found?
5) Graph the electric field E vs. radial distance r.
6) What force would act on an excess electron (q= -1.60 x 10^-19 C) on the surface of the sphere?
7) What is the strength of the electric field at a point 60cm from the center of the sphere?
8) What force would act on an alpha particle (q= +3.20 x 10^-19) located 60cm from the center of the sphere?

Please help by showing work.

Explanation / Answer

From gauss' law,
integral E.Da = qin/e

Assume a sphere of radius r < R1
A of sphere = 4pir^2
E*4pir^2 = 0/e [ as qin = 0]
E = 0

1. E at centre of the sphere = 0 [from formula]

2. E at 10 cm from centre = 0 [from formula]

Assume a sphere of radius R1<r<R2
E*4pi*r^2 = qin/e
qin = Q*v/V
where v volume of sphere containing charge insisde the assumed sphere of radius r
v = 4pi(r^3 - R1^3)/3 =
V is net volume of charged sphere
V = 4pi(R2^3 - R1^3)/3
E*4*pi*r^2 = Q(r^3 - R1^3)/e(R2^3 - R1^3)

3. E = 2*10^-6 (0.3^3 - 0.2^3)/8.85*10^-12 (0.5^3 - 0.2^3) * 4*3.14*0.3^2 = 32465.516 V/m

E = Q(r^3 - R1^3)/e(R3^3 - R1^3)4pir^2
dE/dr = d(r^3 - R1^3)*r^-2 = 0
d(r - R1^3r^-2)/dr = 1 + 2 R1^3*r^-3 = 1 + 2*0.2^3*r^-3 = 0
r would be -ve, so E is max at surface

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.