A solid sphere of radius 21 cm has a total pos- itive charge of 28.7 ìC uniforml

Question

A solid sphere of radius 21 cm has a total pos-
itive charge of 28.7 ìC uniformly distributed
throughout its volume.
a. Calculate the magnitude of the electric field
at the center of the sphere.
Answer in units of N/C.

b. Calculate the magnitude of the electric field
5.25 cm from the center of the sphere.
Answer in units of N/C.

c. Calculate the magnitude of the electric field
21 cm from the center of the sphere.
Answer in units of N/C.

d. Calculate the magnitude of the electric field
37.9 cm from the center of the sphere.
Answer in units of N/C.

Explanation / Answer

a) 0 cm from the center means at the center. The charge is uniformly distributed. Therefore, the electric field at the center = 0.

b) Volume within sphere of radius 5.25 cm = 4/3 * pi * (5.25 cm)^3
Volume of the complete sphere = 4/3 * pi * (21 cm)^3
Charge per unit volume = 28.7/[4/3 * pi * (21 cm)^3] µC
Volume within sphere of radius 5.25 cm = 4/3 * pi * (5.25 cm)^3
Therefore charge with in the sphere of radius 10 cm = charge per unit volume * volume of this sphere
= 28.7/[4/3 * pi * (21 cm)^3] * 4/3 * pi * (5.25 cm)^3 µC
= 28.7 * (21/5.25)^3 µC
= 28.7/4^3 µC
= 28.7/64 µC
= 0.448 µC

For finding electric field, this charge can be assumed to be concentrated at the centre of the sphere. We have to find electric field at the surface of a sphere of radius 5.25 cm = 5..25 * 10^-2 m = 0.0525 with charge 0.448 µC = 0.448 * 10^-6 C at the centre

By Coulomb's law,
the electric field = 9 * 10^9 * 0.448 * 10^-6/( 0.0525)^2
= 9 * 10^9 * 0.448 * 10^-6/0.0525^-2
= 11.1132 N/C

c) The point is at the surface of the sphere.
Total charge = 28.7 µC =28.7 * 10^-6 C
Distance from the centre = 21 cm = 21 * 10^-2 m = 0.21 m
By coulomb's law,
electric field = 9 * 10^9 *28.7 * 10^-6/( 0.21)^2
5857142.587 N/C

d) The point is outside the sphere.
Total charge = 28.7 µC = 28.7 * 10^-6 C
Distance from the centre = 37.9 cm =37.9 * 10^-2 m =0.379 m
By coulomb's law,
electric field = 9 * 10^9 * 28.7 * 10^-6/(0.379)^2
1798233.095 N/C

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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