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Chapter 4: Q12E (page 809)

A cylindrical capacitor has an inner conductor of radius 2.2 mm and an outer conductor of radius 3.5 mm. The two conductors are separated by vacuum, and the entire capacitor is 2.8 m long.

(a) What is the capacitance per unit length?

(b) The potential of the inner conductor is 350 mV higher than that of the outer conductor. Find the charge (magnitude and sign) on both conductors.

Short Answer

Expert verified

The capacitance per unit length is 120.0pF/m.

The charge of the inner conductor is Q = +118pC and outer conductor is Q - 118pC

Step by step solution

01

About capacitance per unit length.

The potential V between the cylinders is not affected by the presence of

the charged outer cylinder and the capacitance per unit length C/L is given by

Now we can plug our values forandinto equation(1)

Hence, the capacitance per unit length is 120.0pF/m.

02

Calculation of charge when potential is given.

We are given the potential of the inner conductor V = 350 mV and higher than that of the outer conductor, which means the positive charge is on the inner conductor and the negative charge is on the outer conductor. To find the charge Q we can use the equation

Hence, the charge of the inner conductor is Q = +118pC and outer conductor is Q - 118pC.

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Most popular questions from this chapter

The capacity of a storage battery, such as those used in automobile electrical systems, is rated in ampere-hours .(A‐h)‐A50A‐hA battery can supply a current of50Afor 1.0h,or25Afor2.0hor for and so on. (a) What total energy can be supplied by a 12-v,60-A‐hbattery if its internal resistance is negligible? (b) What volume (in litres) of gasoline has a total heat of combustion equal to the energy obtained in part (a)? (See Section 17.6; the density of gasoline is 900kg/m3.) (c) If a generator with an average electrical power output ofrole="math" localid="1655719210000" 0.45kW is connected to the battery, how much time will be required for it to charge the battery fully?

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Fig. E25.30.

The energy that can be extracted from a storage battery is always less than the energy that goes into it while it is being charged. Why?

The circuit shown in Fig. E25.33 contains two batteries, each with an emf and an internal resistance, and two resistors. Find (a) the current in the circuit (magnitude and direction) and (b) the terminal voltage Vabof the 16.0-V battery.

Fig. E25.33
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