1)An insulating sphere of radius a=4 cm has charge Q=10 uC uniformly distributed
ID: 2123873 • Letter: 1
Question
1)An insulating sphere of radius a=4 cm has charge Q=10 uC uniformly distributed throughout.This sphere is surrounded by two concentric conducting shells.The first has an inner rdius of b=7.5cm and an outer radius of c=8.0cm. The seocnd has an inner radius of d=13cm and an outer radius of e=15cm.
(GIVE UNTS IN ALL ANSWERS)
A)Using Gauss's Law , derive the Electric Field at r=3cm?
B)What is the net electric flux through a cubic surface with sides of 9.0cm centered about the insulating sphere?
C)What is the Electric field at (i) r=10 cm; (ii)r=14cm and r=15 cm?
D)What, if any, is the total surface charge density on the inner surface of the outer conducting shell?
E)If excess negative charge is placed onto the smaller of the two conducting shells so that the electric field for r>15 cm is zero, how large must that charge density be?
Explanation / Answer
1)
a)charge inside sphere upto radius r = 3 cm
is q= 10*(3^3)/(4^3) = 4.21875 uC
Electric Field at r=3cm = Kq/r = 9*10^9 *4.21875*10^-6 /0.03 = 1.2656*10^6 N/C
b)charge inside cube = 4.21875 uC +(10*(8^3 -7.5^3)/(4^3)) = 5.62695 uC
flux = q/epsilon 0 = 5.62695*10^-6)/(8.854*10^-12) = 0.6355*10^6 Nm^2 /C
c)Electric field at
(i) r=10 cm;
charge inside 10 cm radius, = 5.62695 uC
field = Kq/r = 5.62695*10^-6 *9*10^9 /0.01 = 5.06*10^6 N/C
(ii)r=14cm
charge inside 14 cm radius, = 5.62695 + (10*(14^3-13^3)/(4^3)) = 91.0957 uC
field = Kq/r = 9*10^9 *91.0957*10^-6 / 0.14 = 5.856*10^6 N/C
and r=15 cm
charge inside 15 cm radius, = 5.62695 + (10*(15^3-13^3)/(4^3)) = 189.68945 uC
field = Kq/r = 9*10^9 * 189.68945*10^-6 / 0.15 = 11.38*10^6 N/C
D)charge on inner surface of the outer conducting shell = 5.62695 uC
total surface charge density on the inner surface of the outer conducting shell = (charge)/area
= 5.62695 *10^-6 /(4*pi*0.13^2 ) = 2.6496*10^-5 C/m^2
E)the negative charge that has to be kept onto the smaller of the two conducting shells so that the electric field for r>15 cm is zero, = 189.68945 uC
so, charge density = (189.68945 *10^-6)/(4*pi*0.08^2) = 2.358*10^-3 C/m^2
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.