Question

The figure shows a spherical shell with uniform volume charge density ρ = 1.88 nC/m3, inner radius a = 9.70 cm, and outer radius b = 3.4a. What is the magnitude of the electric field at radial distances (a) r = 0; (b) r = a/2.00, (c) r = a, (d) r = 1.50a, (e) r = b, and (f) r = 3.00b?

Answer 1

inner radius of the spherical shell a = 9.70 cm =9.70*10^-2 m

outer radius of the spherical shell b=3.4a =33*10^-2 m

volume charge density = 1.88 nC/m³ =1.88*10^-9 C/m³

let the radius of the Gaussian surface is r.

at a r b, the enclosed charge q =()(4/3)(pi)[(r³ - a³)]   ...... (1)

therefore electric field is given by

E =k[q/r²]   ......... (2)

where, k =1/4pio

eq (2) becomes

E =[/3o][(r³-a³)/r²]     .......... (3)

a)

given r =0

so, the charge q lie on the surface of the shell is equal to zero.

then the electric field E =0 N/C

b)

given r =a/2

at this point the charge is also zero.

therefore electric field E =0 N/C

c)

similarly at r=a , the charge q =0 C

hence E =0 N/C

d)

given r =1.5a

and permitivity of the free space o = 8.85*10^-12 C²/N.m²

electric field E =[/3o][(r³ - a³)/r²]

E = [1.88*10^-9 / 3*8.85*10^-12 ][0.00308 - 0.00091 / 0.021]

E = 7.31 N/C

e)

given r = b =33*10^-2 m

electric field E =[/3o][(b³ - a³)/r²]

E = [ 1.88*10^-9 /3*8.85*10^-12 ] [0.0359 - 0.000912 / 0.1089]

E = 22.75 N/C

f)

e)

given r = 3b =3*33*10^-2 m

electric field E =[/3o][(b³ - a³)/r²]

E = [ 1.88*10^-9 /3*8.85*10^-12 ] [0.970 - 0.000912 / 0.9801 ]

E = 70.01 N/C