24.13. A spherical capacitor contains a charge of 3.30 nC when connected to a potential differen

step 1 In the given problem, we are having a spherical capacitor in which there are two concentric sphe

24.13. A spherical capacitor contains a charge of 3.30 nC...

24.13. A spherical capacitor contains a charge of 3.30 $\mathrm{nC}$ when connected to a potential difference of 220 $\mathrm{V}$ . If its plates are sepa- rated by vacuum and the inner radius of the outer shell is $4.00 \mathrm{cm},$ calculate: (a) the capacitance; (b) the radius of the inner sphere; (c) the electric field just outside the surface of the inner sphere.

Key Concepts

Charge-Voltage-Capacitance Relationship

The relation Q = CV forms the basis for understanding capacitors, linking the stored charge (Q), the potential difference (V), and the capacitance (C). This fundamental principle allows one to compute one of these quantities when the other two are known, and it is central to solving many problems in electrostatics.

Electric Field in and around a Conductor

The electric field just outside a charged conductor can be determined using Gauss's Law and by considering the symmetric distribution of charge. In the context of a spherical capacitor, calculating the field near the inner sphere reveals important information about the effect of curvature on field strength and how it relates to the stored charge.

Spherical Capacitor

A spherical capacitor consists of two concentric spherical conductors separated by a dielectric (often vacuum). Its configuration dictates that the electric field, potential difference, and capacitance are determined solely by the radii of the inner and outer spheres, making it a fundamental example in electrostatics.

Capacitance of a Spherical Capacitor

The capacitance of a spherical capacitor is given by a formula that relates the radii of the inner and outer spheres. This capacitance measures the ability of the capacitor to store charge for a given voltage, emphasizing the geometric dependence as opposed to the parallel plate capacitor where area and separation are key factors.

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