Use the charge distribution and electric field calculated (a) Show that for ?r ? ?R the potential is identical to that produced by a point charge ?Q?. (Take the potential to be zero at infinity.) (b) Obtain an expression for the electric potential valid in the region ?r? ? ?R?. Problem: A nonuniform, but spherically symmetric, distribution of charge has a charge density ? ?? ?) given as follows: Where ??0 = 3?Q?/??R?3 is a positive constant. (a) Show that the total charge contained in the charge distribution is ?Q?. (b) Show that the electric field in the region ?r ? ?R is identical to that produced by a point charge ?Q at ?r = 0. (c) Obtain an expression for the electric field in the region ?r ? ?R?. (d) Graph the electric-field magnitude ?E as a function of ?r?. (e) Find the value of ?r at which the electric field is maximum, and find the value of that maximum field.

Week 5 Physics 2 for Engineering Chapter 24: Capacitance and Dielectrics Capacitors store charge C = Q/V Unit is Farads, 1 Farad = 1 C/V Review: Q = σ A V = Ed Parallel Plate Capacitor C = A Ɛ / 0 C = Q/V = σ A/ Ed = A Ɛ / d 0 Capacitors in series Charge on each capacitor is the same Voltage on each capacitor is different Applied voltage is equal to the sum of voltages on the two capacitors (V = V +V ) 1 2 1/C eq1/C +11C 2 Capacitors in parallel Voltage (potential) on each capacitor is the same Charge on each capacitor is different (Q = Q +Q ) 1 2 C eq +C1 2 Energy stored in capacitor U= (1/2) Q