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## Homework Statement

A point charge, Q, is located @ (0,0,d) above infinite conducting plane that lies in xy plane and is maintained at ground potential. Find:

a.) surface charge density as a function of x and y on conducting plane, and

b.) total charge induced on conducting plane.

## Homework Equations

See below.

## The Attempt at a Solution

Well, I know that the

**E**field is upward directed in the z-direction because the

**E**-field is always perpindicular to a conducting surface. The answer is in the back of the book, and it is:

a.) ρ

_{s}= (-2Qd)/(4*pi*[ρ

^{2}+ d

^{2}]

^{(3/2)}

b.) Q

_{surface}= -Q

In part a, I do not see how the author got [ρ

^{2}+ d

^{2}]

^{(3/2)}in the denominator of this formula. This equation shows up in the

**E**-field equation for a uniform disc of charge, and how can we assume this?! If I were to follow this implementation, assuming I can follow the assumptions for an uniform disc of charge,

**r**= d

**a**, and

_{z}**r'**= x

**a**+ y

_{x}**a**. (

_{y}**r**-

**r'**) = d

**a**- x

_{z}**a**- y

_{x}**a**. The magnitude of this term to the third power (still following equations for uniform disc of charge) = sqrt(d

_{y}^{2}+ x

^{2}+ y

^{2}) = sqrt(d

_{2}+ ρ

^{2}).

I get stuck here. If someone could let me know if I should continue to follow this method, and if so, how to continue. If I should try another way of thinking, please offer some tips to get me going in the right direction. Thank you for all help, it's most appreciated!