2.32 A cylindrical capacitor has two co-axial cylinders of length 15 cm and radii 1.5 cm and 1.4 cm. The outer cylinder is earthed and the inner cylinder is given a charge of 3.5 μC. Determine the capacitance of the system and the potential of the inner cylinder. Neglect end effects (i.e., bending of field lines at the ends).

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    alok kumar singh | Contributor-Level 10

    3 months ago

    2.32  Length of the co-axial cylinder, l = 15 cm = 0.15 m

    Radius of the outer cylinder, r1 = 1.5 cm = 0.015 m

    Radius of the inner cylinder, r2 = 1.4 cm = 0.014 m

    Charge on the inner cylinder, q = 3.5 μC=3.5×10-6 C

    Capacitance of a co-axial cylinder of radii r1 and r2 is given by the relation

    C = 2πε0lloge?r1r2 , where ε0 = permittivity of free space = 8.854 ×10-12 C2N-1 m-2

    C = 2π×8.854×10-12×0.15loge?0.0150.014 = 1.21 ×10-10 F

    Potential difference of the inner cylinder is given by

    V = qC = 3.5×10-61.21×10-10 = 2.893 ×104 V

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