A particle with a charge of -60.0 nC is placed at the center of a nonconducting

Question

A particle with a charge of -60.0 nC is placed at the center of a nonconducting spherical shell of inner radius 19 cm and outer radius 31.0 cm. The spherical shell carries charge with a uniform density of -1.18 microC/m3.

(a) What is the electric field strength just barely inside the surface of the nonconducting shell?
N/C

(b) What is the total amount of charge on the nonconducting shell?
C

To answer the next three questions, it is useful to find an expression for the electric field strength inside the nonconducting shell as a function of distance from the center of the shell.

(c) What is the electric field strength at a distance of 22 cm from the center of the shell?
N/C

(d) What is the electric field strength at a distance of 25 cm from the center of the shell?
N/C

(e) What is the electric field strength at a distance of 28 cm from the center of the shell?
N/C

(f) What is the electric field strength just barely outside the surface of the nonconducting shell?
N/C

(g) Suppose a proton were to have a circular orbit just outside the spherical shell. Calculate the speed of this proton.

Explanation / Answer

a)

field due to shell inside shell is zero

hense

E = k*q1/r^2 = 9*10^9*-60*10^-9/0.19^2 = -14958.4487 N/m

b)

Volume of shell = 4/3*pi*(R2^3-R1^3) = 4/3*pi*(0.31^3-0.19^3)

charge on shell = d*V = -1.18*10^-6* 4/3*pi*(0.31^3-0.19^3) = -1.133*10^-7 C

c)

E inside spherical shell is given by formula

E = q/(4*eo*R)

q = charge placed at centre +charge due to shell

at R = 22 cm = 0.22 m

E = ((-60*10^-9)-(1.133*10^-7))/(4*8.854*10^-12*0.22) = -22242.1299 N/m

d)

at R = 25 cm = 0.25 m

E = (-60*10^-9-1.133*10^-7)/(4*8.854*10^-12*0.25) = -19573.0743 N/m

e)

at R = 28 cm = 0.28 m

E = (-60*10^-9-1.133*10^-7)/(4*8.854*10^-12*0.28) =-17475.9592 N/m

f)

E = k*(q)/r^2 = 9*10^9*((-60*10^-9)-(1.133*10^-7))/0.31^2 = -16229.9687 N/m

g)

F =Eq

so,

mV^2/r = E*q .......

V = sqrt(E*q*r/m)

V = sqrt(16229.9687*1.6*10^-19*0.31/(1.67*10^-27)) =694290.853 m/s

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