Question

Two curved plastic rods are shaped into semicircles and together they form a circle. The rod on top has a uniform charge distribution of +4Q and bottom rod has a charge of -2Q. What is the net electric field at the center of the circle?

Answer 1

`Electric\ field = (4KQ )/(\pi R^2)`

Step-by-step explanation:

Given that

Top rod have +4Q charge

Bottom tube have -2Q charge

We know that electric filed due to half ring on the center given as

`E=(2K\lambda )/(R)`

Where

λ is the charge per unit length

K is the constant

R is the radius of ring

For top rod

λ=+4Q/πR

So

`E=(2K* 4Q )/(\pi R^2)`

`E=(8KQ )/(\pi R^2)`

For bottom ring

`E'=-(2K* 2Q )/(\pi R^2)`

`E'=-(4KQ )/(\pi R^2)`

So the total resultant electric field at the center= E-E'

`Electric\ field = (8KQ )/(\pi R^2)-(4KQ )/(\pi R^2)`

`Electric\ field = (4KQ )/(\pi R^2)`