Question

A proton traveling along the x-axis enters a region at x = 0 where the x-component of the electric field is given by E = Ao/x1/2. How much work is done on the proton by the electric field as it moves along the x-axis from x = 0 to x = 7 m?

Answer 1

.Answer:

The value of the work done is
`\bf{ 5.29 qA_(0)}`.

Step-by-step explanation:

When a charged particle having charge
`q` is moving through an electric field
`E`, the net force (
`F`) on the charge is

`F = qE~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(1)`

and the work done (
`W`) by the particle is

`W = \int\limits^x_0 {F} \, dx ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(2)`

Given,
`E = (A_(0))/(x^(1/2))`.

Substitute the value of electric field in equation (1) and then substitute the result in equation (2).

`W &=& \int\limits^7_0 {q(A_(0))/(x^(1/2))} \, dx \\&=& qA_(0) \int\limits^7_0 {x^(-1/2)} \, dx \\&=& 2qA_(0)[x^(1/2)]_(0)^(7)\\&=& 5.29 qA_(0)`