Question

A charged wire of length L lies along x-axis in such a way that its linear charge density is given by lambda=ax square where a is constant .Calculate charge on wire.

Answer 1

lemda =charge /unit length where lemda =ax^2 then charge integrate(dq) =integrate(ax^2dl) dq ko 0 to q tak integrate and Rhs ko 0to l length then q =al^3/3 this the ans

Answer 2

Answer:

Charge on the wire will be equal to (1/2)aL² where L is the length of wire.

Explanation:

Consider that a wire AB of length L.

Given, Linear charge density of wire $=\lambda$

We have given, $\lambda =ax$

Consider a small volume element of length dx has charge dq,

$dq=\lambda.dx$                                                        ................(1)

Put the value of $\lambda$ in eq.(1) and integration both sides:

$\int\limits^q_0 {dq} =\int\limits^L_0 {ax.} \, dx$

$\int\limits^q_0 {dq} =a\int\limits^L_0 {x.} \, dx$

$q=a[\frac{x^{2}}{2} ]^{L}_{0}$

$q=\frac{1}{2}aL^{2}$