Question

At a distance D from a very long (essentially infinite)uniform line of charge, the elecric field is 1000 N/C. Forthe field strength to be 2000 N/C, the distance from the line wouldhave to be:a. D/√2b. √2Dc. D/2d. 2De. D/4

Answer 1

The answer is A

Step-by-step explanation:

Electrical field formula is:

`F=2*k*q/D[tex]F=2*k*q/D^2=1000\\F=2*k*q/(D/√(2)) ^2=2000`

To increase the electrical field from 1000 N/C to 2000 N/C when the q is constant the distance would have to be:

Answer 2

A

Step-by-step explanation:

The electric field = 1000N/C

Using the formula

F = q/4πeD^2 where F is the force experience by a charge body brought from infinity to D and e is the field constant in C/N.m^2 and D is the distance from the uniform field

1000 = q/4πeD^2

Make q subject of the formula

1000*(4πeD^2) = q

If the force changes to 2000 then equation changes to:

2000 = q /4πeD1^2 where D1 is the new distance

Substitute q in equation 2

2000 = 1000*(4πeD^2) / 4πeD1^2

Cancel 4πe

2000 = 1000 * D^2 / D1^2

Cross multiply and make D1^2 subject of the formula

D1^2 = 1000D^2/ 2000

D1^2 = D^2/2

Take square root of both side

D1 = √(D^2/2) = D / √2