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Chapter 16: Problem 60

A conductor in electrostatic equilibrium contains a cavity in which there are two point charges: \(q_{1}=+5 \mu \mathrm{C}\) and \(q_{2}=-12 \mu \mathrm{C} .\) The conductor itself carries a net charge \(-4 \mu C .\) How much charge is on (a) the inner surface of the conductor? (b) the outer surface of the conductor?

Short Answer

Expert verified
Answer: The charge on the inner surface of the conductor is -7μC and the charge on the outer surface of the conductor is 3μC.

Step by step solution

01

Calculate the total charge inside the conductor cavity

We have two point charges inside the cavity: \(q_1=+5\mu C\) and \(q_2=-12\mu C\). To find the total charge inside the cavity, add these point charges together: $$Q_\text{cavity} = q_1 + q_2 = (+5\mu C) + (-12\mu C) = -7\mu C$$
02

Calculate the charge on the inner surface of the conductor

Since the total charge inside the cavity will equal the charge induced on the inner surface of the cavity, the charge on the inner surface of the conductor is: $$Q_\text{inner} = Q_\text{cavity} = -7\mu C$$
03

Calculate the charge on the outer surface of the conductor

To find the charge on the outer surface of the conductor, we need to consider that the net charge on the conductor is \(-4\mu C\). Since the charge on the inner surface has already been determined, the charge on the outer surface can be found as follows: $$Q_\text{outer} = Q_\text{total} - Q_\text{inner} = (-4\mu C) - (-7\mu C) = 3\mu C$$ The charge on the inner surface of the conductor is \(-7\mu C\), and the charge on the outer surface of the conductor is \(3\mu C\).

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