Question

For the configuration shown in the figure below, suppose a -5.00 cm, b = 20.0 cm, and c = 25.0 cm. Furthermore, suppose the electric field at a point 12.0 cm from the center is measured to be 3.75 X 10' N/C radially inward and the electric field at a point 50.0 cm from the center is of magnitude 202 N/C and points radially outward. From this information, find the following. (Include the sign of the charge in your answer.) Insulator Conductor (a) the charge on the Insulating sphere -6.000.09 C (b) the net charge on the hollow conducting sphere 1.2e-09 X What is the total charge inside a sphere of radius 50 cm?

Answer 1

a)

Electric field at distance
r = 12 cm = 0.12 m
from the center is
E = -3.75 * 103 N/C
(negative sign indicates direction is radially inward)

For a Gaussian sphere of radius
r = 12 cm
, only charge enclosed is charge on the insulating sphere $Q_1$.

Since the charge is distributed with spherical symmetry, the insulated sphere can be replaced by a point charge located at center.

Electric field at
r = 12 cm
due to the charge on insulating sphere is
E ARE TER2Q1 = 47€or?

Q1 = (0.12)-(-3.75 * 103) 8,99 * 109 = -6.007 * 10-90

b)

Electric field at distance
r = 50 cm = 0,50 m
from the center is
E = 202 N/C
(positive sign indicates direction is radially outward)

For a Gaussian sphere of radius
r = 50 cm = 0,50 m
, charge enclosed is charge on the insulating sphere $Q_1$.and charge on the hollow conducting sphere.

Since the charge is distributed with spherical symmetry, the hollow conducting sphere can be replaced by a point charge located at center.

Electric field at
r = 50 cm
due to the two charges is
ΕΞΑπεργ2T 4περν2

Q2 = 47€or? (E - A1072)

0.50? Q2 = s.99 + 109 | 202 - 8.99 + 10 + -6.007 + 10-9 0.502

$Q_2=11.62*10^{-9}\,C$

Charge on hollow conducting sphere is $Q_2=11.62*10^{-9}\,C$