You are given the following electric field distribution in s

You are given the following electric field distribution in sphere space (x, p1g, a, b, c are given a, b and c are in meters) E in v/m = 0 r

(a) at r=a

LHS= left hand limit= limi h-->0 E(a-h)= 0

RHS = right hand limit

= limit h-->0. E(a+h)

= x/(4*epsilon*a^2)

As LHS= RHS

Hence Electric field is not defined at r=a. Or Electric filed is discontinuous at at r=a.

At r=c

LHS= left hand limit

=limit h-->0 E(c-h)

= x/(4*epsilon*c^2)+(c^3-b^3)*p1/(3*epsilon*c^2)

RHS = right hand limit

=limit h-->0 E(c+h)

= x/(4*epsilon*c^2)+(c^3-b^3)*p1/(3*epsilon*c^2)

As RHS= LHS , hence

E(r=c)=x/(4*epsilon*c^2)+(c^3-b^3)*p1/(3*epsilon*c^2)

(b) unit of x= coulomb

Unit of p1=charge density=coulomb/m^3

= x, r<a

= 0, a<r<b

=4* p1(c^3-b^3)/3, b<r<c ,

= 0 , c<r<d

= 9, r>d

Cd=Charge distribution

=x/(4a^3), coulomb per unit volume, r<a

= p1 coulomb per unit volume, b<r<c ,

= 0 , c<r<d,

=9/(4d^2) coulomb Per unit area, r>d