0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

A solid sphere of radius a has volume charge density p given by p=p1,0ra2 =p2,a2ra and electric potential at center is twice as electric potential at surface:
  1. p1=2p2
  2. p1=3p2
  3. p1=5p2
  4. p1=p2

A
p1=p2
B
p1=5p2
C
p1=2p2
D
p1=3p2
Solution
Verified by Toppr

0ra2:ρ=ρ1
a2ra:ρ=ρ2
The system is equivalent to two solid spheres (i) radius a, density ρ2 (ii) radius a2, density (ρ1ρ2).
potential at O:Vo=14πεo.32.4πa33ρ2a+14πεo.32.4π3a38×(ρ1ρ2)×2a
=a2ρ22εo+a28εo(ρ1ρ2)=a28εo(ρ1+3ρ2)
Potential on the surface at P :
VP=14πεo.4πa33ρ2a+14πεo.4π3a38(ρ1ρ2)a
=a2ρ23εo+a2(ρ1ρ2)24εo=a224εo(8ρ2+ρ1ρ2)
a224εo(ρ1+7ρ2)
Vo=2Vp, then, 2(ρ1+7ρ2)=(3ρ1+9ρ2)
i.e., 2ρ1+14ρ2=3ρ1+9ρ2
ρ=5ρ2

Was this answer helpful?
0
Similar Questions
Q1
A solid sphere of radius a has volume charge density p given by p=p1,0ra2 =p2,a2ra and electric potential at center is twice as electric potential at surface:
View Solution
Q2

Half of the rectangular plate shown in figure is made of a material of density p1 and the other half of density p2. The length of the plate is L. Locate the centre of mass of the plate.


View Solution
Q3
Two point P1 and P2 are at distances 'r' and 3r respectively from a point charge. What is the ratio of electric field intensities at these points P1 and P2 ?
View Solution
Q4

Half of the rectangular plate shown in figure is made of a material of density p1 and the other half of density p2. The length of the plate is L. Locate the centre of mass of the plate.


View Solution
Q5
Two electric bulbs, rated at (40 W, 220 V) and (160 W, 220 V) are connected in series at 110 V. If power drawn by bulb 1 (40 W) is P1 & bulb 2 (160 W) is P2, then
View Solution