Charges And Conducting Sheet

Electricity and Magnetism Level 4

Two charges are placed above an infinite conducting sheet as shown. The first has charge $-6q$ and is placed a distance $d$ above the sheet, whereas the second has charge $6q$ and is placed a distance $d$ directly above the first (so that it is a total distance $2d$ away from the sheet).

Where $k = 1/(4\pi\epsilon_0)$ , suppose $F = C \cdot kq^2/d^2$ represents the magnitude of the force on the first charge (of charge $-6q$ ). What is $C$ ?

The answer is 31.

1 solution

Lawrence Chiou
Mar 16, 2016

By the method of image charges, Laplace's equation is satisfied for the configuration if image charges of charge $6q$ and $-6q$ are placed, respectively, a distance $d$ and $2d$ below the sheet, collinear with the two charges above the sheet.

Such a configuration leads to a net force on the charge of $-6q$ of

$F = k\frac{36q^2}{d^2} - k\frac{36q^2}{4d^2} + k\frac{36q^2}{9d^2} = 31k\frac{q^2}{d^2}.$

Therefore, $C = 31$ .

I think answer should be 41 as you have mistaken in sign and direction. Please check it.

Navneet Prabhat - 4 years, 7 months ago

I think this method is valid only when the infinite sheet is grounded.

Am i right or there's something more to it?

neelesh vij - 5 years, 1 month ago

In this case, the result is the same regardless of whether the sheet is grounded. See, for instance, https://www.physicsforums.com/threads/point-charge-above-infinite-conducting-plane.775088/

Lawrence Chiou - 5 years, 1 month ago

Do and is correct

Satyam Tripathi - 4 years, 6 months ago

Charges And Conducting Sheet

The answer is 31.

1 solution

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