Potential Energy of Capacitor - Higher Physics - Solved Past Paper, Exams of Physics

Download Potential Energy of Capacitor - Higher Physics - Solved Past Paper and more Exams Physics in PDF only on Docsity! Answer 1 (a) Q' = Q, the charge remains the same, since there is nowhere for the charge to flow. 2 CHK. 2 VW =V/r, since V = Q/C and C has increased. « BE! = E/x, since H = V/d and V has decreased. « U' =U/x, since U = CV?/2. (b) » Q’ =Q, the charge remains the same, since there is nowhere for the charge to flow. sorte * C’ = 20, since we now have effectively the Seer combination of two capacitors, each with 4 times the original capacitance. « V'=V/2, since V = Q/C and C has doubled. © E! = 2F in the two air gaps, since B = V/d and V has halved while d has gone dome” by a factor of four. # is zero in the conductive slab. © 0 =0, since U = CVv?/2 L (c) Since the potential energy of the capacitor on the left is Jess with the slab inserted, it means \23\ that energy is required to remove the slab. This energy will come a retarding force which only acts in the opposite direction to gravity. So, the slab will accelerate at less than g. The conductive slab on the right has no effect on the stored energy, and so will accelerate at g. Answer 2 (a) Choose a gaussian surface which is a sphere, radius 7, contered on. the given sphere. By Ganiss’ Law. . . : (by Since there are no charges enclosed within the cavity, by Gauss” Law the electric field is constant within it. So, we only need to calculate # at one point. Let's use the centre of the cavity, for simplicity. Ry the superimposition principle, the electric field is the sum of the original whole sphere, plus a sphere the same size/position as the cavity but with a charge density of —p. Bub the . field in the centre of the 2nd sphere is zoro, from the result of part (a), therefore the field throughout the cavity is simply # at its centre, as if the cavity was not there, i.e., pa deo directed radially outwards.’ {c) The charges will be distributed on the outside of the conducting sphere: