Question: Two point charges with charge + q / 2 each are found on the y axis at y = + d and y = d

Two point charges with charge

+

/ 2

each are found on the y axis at y

= +

d and y

=

.

Show that the resultant electric field on the x axis is E

=

Kq x

/ (

2 +

2) 3 / 2

.

(

)

Now suppose there are four charges, each with charge

+

/ 4 .

Two of them are on the y axis at y

= +

d and y

= -

,

and the other two are on the Z-axis at z

= +

d and z

= -

.

Find the electric field on the x axis.

(

)

Finally, suppose instead of point charges, there is a charged ring with radius d and total charge

+

q centered in the yz plane. Argue for and write what the electric field is on the x axis.

(

)

A uniformly charged sheet has area A and total charge Q

.

We then cut out a ring with radius d from the sheet so that a charge q is now missing. What is the electric field along the axis of the cut out ring

(

and close to the sheet

) .

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