Answer to Question #134291 in Electricity and Magnetism for Rohan

Question

Consider three charge distributions
A. ρ (x, y, z) = kx

B. ρ (x, y, z) = k √ (x2 + y2)

C. ρ (x, y, z) = k √ (x2 + y2 + z2)

Here k is a constant. A, B, C are

(a) Planar Symmetric

(b) Planar, Spherically, Cylindrically Symmetric respectively

(c) Spherically, Planar and cylindrically symmetric respectively

(d) Planar, Cylindrically, Spherically symmetric respectively

Answer 1

solution

(A) as $\rho(x\space y\space z)=kx$

is considered then charge is distributed on the x-axis as we can conclude from the equation of distribution. if charge distribution is considered for y and z axis then there will no any charge distribution obtain according to equation. charge distribution will be only vary along x-axis.so charge distribution is in planner symmetry.

(B)as

$\rho(x\space y\space z)=k\sqrt{x^2+y^2}\\$

is considered then charge distribution is in circular plane.this shows that change in charge distribution can be detect in x and y direction only and along z axis there will be no affect. therefore it can be concluded that symmetry of charge distribution is cylindrical.

(C)

as

$\rho(x\space y\space z)=k\sqrt{x^2+y^2+z^2}$

is considered then charge distribution is spherical ,so

symmetry of charge distribution is spherical.

so option (d) is correct according to above explanation.