A ball of radius R carries a positive charge whose volume density at a point is given by 
Where ρ0 is a constant and r is distance from the centre. The value of maximum electric field due to this configuration is
Mithil , 5 Years ago
Grade 12
Electrostatics> A ball of radius R carries a positive cha...
1 Answers
Arun
Last Activity: 5 Years ago
(a) We assume the ball to be divided into infinite number of concentric thin shell of thickness dr. Let us assume such a shell at a radial distance r.
Volume of this shell =pdV=4πr
2
ρdr=4πr
2
ρ
0
(1−
R
r
)dr
Net charge enclosed in the sphere of radius r
q=∫pdv=
0
∫
r
4πρ
0
r
2
(1−
R
r
)dr=4πρ
0
(
3
r
3
−
4R
r
4
)
Electric field at radial distance r
E=
4πε
0
r
2
q
=
4πε
0
r
2
1
×4πρ
0
(
3
r
3
−
4R
r
4
)=
3ε
0
ρ
0
r
(1−
4R
3r
)
Now for those points outside the sphere, we have to take into account the total charge contained in the sphere of radius R.
Total charge Q=
0
∫
R
ρ
0
(1−
R
r
)4πr
2
dr=
3
πρ
0
R
3
Electric field, using Gauss's laws, at a point which is at distance r(>R) from the centre;
∫E.ds=
ε
0
Q
⟹E=
4πε
0
r
2
Q
=
12ε
0
r
2
ρ
0
R
3
(b) Again let us consider the expression for electric field within the sphere of radius R:
E=
3ε
0
ρ
0
r
(1−
4R
3r
)
For maximum electric field:
dr
dE
=0⟹1−
4R
6r
=0⟹r=
3
2R
Putting, r=
3
2R
, value of maximum electric field, E
max
=
9∈
0
ρ
0
R
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Other Related Questions on electrostatics
Electrostatics question based on earthing of spherical shell
Electrostatics question based on earthing of spherical shell
electrostatics
0 Answer Available
Last Activity: 2 Years ago
an object has a charge of 2c and gains 10^19 electrons. the net chaarge on the object becomes??
an object has a charge of 2c and gains 10^19 electrons. the net chaarge on the object becomes??
electrostatics
1 Answer Available
Last Activity: 3 Years ago
A wire with a linear charge density lambda forms a quarter of a cjrclenof radius R and is placed asa shown in thefigure with its centre of curvature at the origin O the electric field at O will be
A wire with a linear charge density lambda forms a quarter of a cjrclenof radius R and is placed asa shown in thefigure with its centre of curvature at the origin O the electric field at O will be
electrostatics
0 Answer Available
Last Activity: 3 Years ago
Find the value of q so that system remains in equilibrium.. figure attached below
Find the value of q so that system remains in equilibrium.. figure attached below
electrostatics
0 Answer Available
Last Activity: 3 Years ago
Find the value of q so that system remains in equilibrium
Find the value of q so that system remains in equilibrium
electrostatics
0 Answer Available
Last Activity: 3 Years ago