Examples 2 - 9702/41/O/N/10: (a) Define capacitance. (b) An isolated metal sphere has a radius r. When charged to a potential V, the charge on the sphere is q. The charge may be considered to act as a point charge at the centre of the sphere.
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(i) State an expression, in terms of r and q, for the potential V of the sphere.
(ii) This isolated sphere has capacitance. Use your answers in (a) and (b)(i) to show that the capacitance of the sphere is proportional to its radius.
(c) The sphere in (b) has a capacitance of 6.8 pF and is charged to a potential of 220 V. Calculate
(i) the radius of the sphere,
(ii) the charge, in coulomb, on the sphere.
(d) A second uncharged metal sphere is brought up to the sphere in (c) so that they touch. The combined capacitance of the two spheres is 18 pF. Calculate
(i) the potential of the two spheres,
(ii) the change in the total energy stored on the spheres when they touch.
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Recorded at MCKL #CambridgeALevelPhysics
9702_w10_qp41
