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workout 25b

# workout 25b - HPHY 253 Workout 25b The Relationship between...

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Unformatted text preview: HPHY 253 Workout 25b The Relationship between the Electric Field and Potential Dr. A. E. Bak Name 1. Serway & Jewett Problem 25 : 31 . Over a certain region of space, the electric potential is given by V = 5 x & 3 x 2 y + 2 yz 2 , where all quantities here are measured in the appropriate SI units. (a) Determine the electric ¡eld over this region. We have @V @x = 5 & 6 xy ; @V @y = & 3 x 2 + 2 z 2 ; @V @z = 4 yz : It follows that E = & r V = & & e x @V @x + e y @V @y + e z @V @z ¡ = (6 xy & 5) e x + ¢ 3 x 2 & 2 z 2 £ e y & 4 yz e z is the electric &eld. (b) What is the magnitude of the ¡eld at the point (1 ; ; & 2) ? At the point in question, the electric &eld is E = [6 (1) (0) & 5] e x + h 3 (1) 2 & 2 ( & 2) 2 i e y & 4 (0) ( & 2) e z = ( & 5 e x & 5 e y ) V =m ; having E = q E 2 x + E 2 y + E 2 z = q ( & 5) 2 + ( & 5) 2 + (0) 2 = 5 p 2 ¡ 7 : 07 V =m as its magnitude. 2. Serway & Jewett Problem 25 : 67 . An uncharged conducting sphere of radius a is placed, centered at the origin, into a region of initially uniform electric ¡eld E e z , where E is a constant. The resulting electric potential is given by V = V for points inside the sphere and by V = V & E z + E a 3 z ( x 2 + y 2 + z 2 ) 3 = 2 for points outside the sphere, where the constant V is the potential on the sphere¢s surface. Determine the resulting electric ¡eld....
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workout 25b - HPHY 253 Workout 25b The Relationship between...

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