Question

Q1) A spherical conductor (radius = 1.0 cm) with a charge of 2.0 pC is within a concentric hollow spherical conductor (inner radius = 3.0 cm, outer radius = 4.0 cm) which has a total charge of -3.0 pC. What is the magnitude of the electric field 2.0 cm from the center of these conductors.

Q2)A charge is uniformly distributed along the entire x-axis. If each 20 cm length of the x-axis carries 2.0 nC of charge. What is the magnitude of the electric field at the point y= 2.0 m, on the y axis?

Q3)A solid nonconducting sphere of radius 12 cm has a charge of uniform density ρ = 6.0 nC/m3 distributed throughout its volume. Determine the magnitude of the electric field 5.0 cm from the center of the sphere

Answer 1

consider a gaussian sphere of radius r = 2 cm

the charge inside the gaussian sphere = q = 2 pC

from gauss law

E*4*pi*r^2 = q/e0

E*4*pi*0.02^2 = 2*10^-12/(8.84*10^-12)

E = 45 N/C

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Q2)

linear charge density lambda = q/l = 2*10^-9/0.2 = 10 nC

electric field E = lambda/(2*pi*e0*y)

E = 10*10^-9/(2*pi*8.84*10^-12*2) = 90 N/C

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Q3)

electric field inside the sphere E = sigma*r/(3*eo)

E = 6*10^-9*0.05/(3*8.84*10^-12) = 11.31 N/C