logo
or
search
upload

A spherical conducting shell of inner radius r_(1) and outer radius r_(2) has a charge Q. <br> (a) A charge q is placed at the center of the shell. What is the surface charge density on the inner and outer surfaces of the shell ? <br> (b) Is the electric field intensity inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape ? Explain.

Apne doubts clear karein ab Whatsapp par bhi. Try it now.
CLICK HERE

Loading DoubtNut Solution for you

Watch 1000+ concepts & tricky questions explained!

23.8 K+ views | 14.0 K+ people like this

   
Share
Share

Answer Text

Solution :
(a) Charge palce at the centre of a shell is +q. hence, a charge of magnitude -q will be induce to the inner surface of the inner surface of the shell. Therefore, total charge on the inner surface of the shell is -q. <br> surface charge density at the inner surface of the shell is given by the realation, <br> `sigma_(1)=("Total charge")/("inner surface area")=(-q)/(4pir_(1)^(2)).....(i)` <br> A charge of +q is induced on the outer surface of the shell. a charge of magnitude Q is place on the outer surface of the shell . therefore , total charge on the outer surface of the shell is +Q+q. surface charge density at the outer surface of the shell, <br> `sigma_(2)=("Total charge")/("Outer surface area")=(Q+q)/(4pir_(2)^(2)).....(ii)` <br> (b) yes <br> The electric field intensitinside a cavity is zero, even if the shell is not spherical and has any irregular shape. take a closed loop such taht a part of it is inside the cavity along a field line while the rest is inside the conductor. net work done by the field in carrying a test charge over a closed loop is zero because the field inside the conductor is zero. hence, electric field is zero, whatever is the shape.

Related Video

3:26

22.7 K+ Views | 1.1 K+ Likes

2:22

110.5 K+ Views | 5.5 K+ Likes

3:14

100.5 K+ Views | 5.0 K+ Likes

13:01

108.8 K+ Views | 5.4 K+ Likes

13:01

41.0 K+ Views | 15.4 K+ Likes

4:17

762.4 K+ Views | 437.2 K+ Likes

bottom open in app