Question

if linear charge density of a wire of length l depends on distance x from one end as lambda is equal to lambda not into x upon L . find total charge of wire

Answer 1

Final Answer : Lambda°L/2
For Calculation see pic

Steps:
1) Since, linear charge density is varying with distance x so, we first find charge for 'dx'length of wire.
dq = integration of Lambda dx
Then, we will integrate it from 0 to L.


For Calculation see pic

Answer 2

Answer:

Total charge, $Q=\dfrac{\lambda_0L}{2}$

Explanation:

Total charge divided by total length is called the linear charge density. Mathematically, it can be given as:

$\lambda=\dfrac{dQ}{dL}$

It is given that,  

$\lambda=\dfrac{\lambda_ox}{L}$

$dQ=\int\limits^L_0 {\lambda} \, dx$

$Q=\dfrac{\lambda_0}{L}\int\limits^L_0 {x} \, dx$

$Q=\dfrac{\lambda_0L}{2}$

Q is the total charge of the wire. Hence, this is the required solution.