A solid sphere of radius 40.0 cm has a total positive charge of 26.9 µC uniforml

Question

A solid sphere of radius 40.0 cm has a total positive charge of 26.9 µC uniformly distributed throughout its volume. Calculate the magnitude of the electric field at the following distances.

(a) 0 cm from the center of the sphere
kN/C

(b) 10.0 cm from the center of the sphere
__________ kN/C

(c) 40.0 cm from the center of the sphere
__________ kN/C

(d) 64.5 cm from the center of the sphere
__________ kN/C

A solid sphere of radius 40.0 cm has a total positive charge of 26.9 © uniformly distributed throughout its volume. Calculate the magnitude of the elec c field at the olow ng distance a) O cm from the center of the sphere kN/C (b) 10.0 cm from the center of the sphere KN/C (c) 40.0 cm from the center of the sphere kN/C (d) 64.5 cm from the center of the sphere kN/C

Explanation / Answer

For sphere of uniform charge

Let r is point where we suppose to find field and R is the radius

For r<R

E=Qr/4×pi×permitivity×R^3..........eq1

R=40cm ,Q=26.9×10^-6C

At 0cm from center using eq 1

put r=0 cm

We get E=0

At 10cm from center

r=10cm=0.1m,R=0.4m

Using eq 1 we get

E=26.9×10^-6×9×10^9×0.1/(0.4)^3=3.78×10^5N/C

At R=40cm

Put r=R=0.4 using eq 1 we get

E=26.9×10^-6×9×10^9/(0.4)^2=15.13×10^5N/C

At r=64.5cm=0.645m

For r>R

E=Q/4×pi×permitivity×r^2=26.9×10^-6×9×10^9/(0.645)^2=5.82×10^5N/C

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