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Review 1 Topics 2 Electric field, dielectrics and conductors Problem 21.54 Problem 22.39 Problem 22.70 Problem 23.64 Problem 23.63 Electric field, dielectrics & conductors 3 Electric field By definition, it points in the direction of motion of a positive point charge Dielectrics Molecules are polarized by an external electric field Conductors In equilibrium, E = 0 within conductor Problem 21.54 An infinitely long rod of radius R carries a uniform volume charge density r. Show that the electric field is E = r R2/(2e0 r) E = r r/(2e0) 4 r>R r<R …21.54 Gauss’s law E dA Q / e 0 is always true. However, because this problem has cylindrical symmetry, the law can be used to find the electric field within and outside the rod by using concentric Gaussian surfaces R r 5 Problem 22.39 Electrons in a TV tube are accelerated from rest across a potential difference of 25 kV. Compute the speed with which the electrons hit the TV screen. me = 9.1 x 10-31 kg |e| = 1.6 x 10-19 C 6 Hint: conservation of energy Problem 22.70 A conducting sphere of radius R1 carries a charge Q1. It is surrounded by concentric spherical shell of radius R2 carrying charge Q2. Compute the potential at the sphere’s surface, choosing the potential at infinity to be zero. 7 … 22.70 There are two ways to approach this problem: 1. Compute the potential for the sphere and the shell separately and add the potentials. Remember: the potential is always with respect to some reference value (e.g., zero at infinity). 2. Compute the potential at the sphere’s surface directly from B 8 V E dr A Problem 23.64 A sphere radius R carries a charge Q spread uniformly over its surface. Show that the energy stored in its electric field is U = k Q2/2R 9 … 23.64 This can be done in different ways: e.g., given the energy density u = e0 E2/2, write dU = udv, where dv = 4pr2dr is a thin shell of radius r and thickness dr. Then sum dU. Note: E k Q r 2 10 U udv e0 e0 Q 2 k 4 p r dr 2 2 r 4p k Q 2 2 2 2 2 1 kQ r R 2R Problem 23.63 A sphere radius R carries a charge Q spread uniformly through its volume. Show that the energy required to assemble the charge is U = 3k Q2/5R while the energy stored within the sphere is U = kQ2/10R 11 Problem 23.63 A sphere radius R carries a charge Q spread uniformly through its volume. Show that the energy required to assemble the charge is U = 3k Q2/5R while the energy stored within the sphere is U = kQ2/10R 12 … 23.63 The total potential energy of the charge is given U V dq where V k q and q r 4 pr 3 3 r dq r 4p r dr 2 putting together the pieces we get U Vdq 13 3 kQ 5R 2 Note: this is the energy within the sphere as well as outside