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EE140 Fall 2014 Mid Term 1 Dr Ray Kwok Name Last First 1 A line charge of length 10 m along the z axis from z 5 to 5 m has a linear charge density of 2 z What is the electric potential and electric field intensity at 1 0 0 m dq dz z r x 5 kdq k dz r r 5 k 2 z dz V x 2 4k 2 2 z x 0 dV 5 z 2 5 x 2 0 4k 25 x 2 x r V x x E x x 4k 1 x 4k 1 x 2 2 x 25 x 25 x V 1 4k 25 12 1 16 4k 148 GV 1 E 1 4k 1 x 3 22kx 28 9 x 25 12 GV m EE140 Fall 2014 2 Mid Term 1 Dr Ray Kwok a A wire of length L along the z axis from z L 2 to L 2 is carrying a dc current I in the zdirection What is the magnetic field intensity B at the point x 0 0 b Use this result to evaluate the B field right above the ground plane at point A as shown in the figure use Biot Savart Law to calculate the B field at x 0 0 r r o Id l r o Idz cos dB 4 r 2 4 r2 r I L 2 cos dz B o 4 L 2 r 2 L 2 dl dz z r z x tan x dz x sec 2 d r x sec r I L 2 x sec 2 cos d o I B o 2 sin m o I 2 2 4 L 2 x sec 4 x 2 x L 2 wire with current I length L L 2 x 2 L 2 The effect of the ground plane is captured by the image current direction as shown As a result the magnetic field at point A x L 2 is just doubled L 2 o 45 A Infinite ground plane Image current I r L 2 Btotal 2 o 2 2 x x 2 L 2 r o I L 2 Btotal L 2 L 2 2 L 2 2 r Btotal 2 o I L 2 EE140 Fall 2014 3 Mid Term 1 Dr Ray Kwok A dielectric sphere with dielectric constant r of radius a is filled with positive charges of non uniform volume charge density r where is a constant A conducting shell of inner radius b and outer radius c is shielding the dielectric as shown in the Figure The outer shield is grounded at r c as shown a Calculate the electric field in all regions b Sketch E r as a function of r Label all axes What are the magnitude of E at r a at r b and at r c c b a a r a EA Qenclosed E r r o E 4 r