# Finding the charge on the outer surface of the conductor

#### mr_coffee

Hello everyone. I'm having troubles getting the last part of this question. An isolated conductor of arbitreary shape has a net charge of +10x10^-6C. Inside the conductor is a cavity within which is a point charge q = +3.0x10^-6C. What is the charge (a) on the cavity wall and (b) on the outer surface of the conductor?

I got (a) which is -3.0x10^-6C because the charge insdie a conductor has to be 0. But (b) is +1.3x10^-5C. I have no idea how they came up with this.

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#### geosonel

mr_coffee said:
Hello everyone. I'm having troubles getting the last part of this question. An isolated conductor of arbitreary shape has a net charge of +10x10^-6C. Inside the conductor is a cavity within which is a point charge q = +3.0x10^-6C. What is the charge (a) on the cavity wall and (b) on the outer surface of the conductor?

I got (a) which is -3.0x10^-6C because the charge insdie a conductor has to be 0. But (b) is +1.3x10^-5C. I have no idea how they came up with this.
charges on a conductor can only exist on the surfaces (like the outer surfaces, or the wall surface of an internal cavity). the problem states the total NET charge on the conductor (surfaces) is +10x10(-6) Coulombs. since you've already correctly determined the internal cavity surface charge to be -3.0x10(-6) C, the remainder must be on the outer surface:
outer surface charge = (total NET charge) - (inner cavity surface charge)
= (+10x10(-6)) - (-3.0x10(-6))
= +1.3x10(-5) C

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#### mr_coffee

awesome thanks, but i don't understand why in your calculation you included the negative sign with the charge, i thought it has no mathamatical significance?

#### geosonel

mr_coffee said:
awesome thanks, but i don't understand why in your calculation you included the negative sign with the charge, i thought it has no mathamatical significance?
charge sign ("+" or "-") is generally significant and should be included in your calculations.

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