A cylindrical capacitor has an inner conductor of radius 1.5 mm andan outer conductor of radius 3.4 mm. The two conductors are separated by vacuum, and the entirecapacitor is 3.0 m long.(a) What is the capacitance per unit length?F/m(b) The potential of the inner conductor is 350 mV higher than thatof the outer conductor. Find the charge (magnitude and sign) onboth conductors.

Part(a): The capacitance per unit length of the capacitor is .

Part(b): The charge in the inner shell is and the charge of the outer shell is .

Explanation:

Part(a):

The capacitance () per unit length of a cylindrical capacitor is given by

where '' is the permittivity of free space, '' is the radius of the outer shell and '' is the radius of the inner shell.

Given, and . We know, . Substituting the values in the above equation,

Part(b):

As the voltage on the inner conductor is higher than that of the outer conductor, positive charge resides on the inner shell and negative charge resides on the outer shell.

The charge '' of a capacitor of length '' having capacitance '' and potential difference '' is given by

Given, and . Substituting these values in the above expression

The charge in the inner shell is and the charge of the outer shell is .

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