EE140 MT2B Spring 2022 Dr Ray Kwok Name EE140 MT2B Spring 2022 Dr Ray Kwok 1 35 pts A point charge Q is placed at u 0 0 along the x axis as shown in the figure The yz plane is an infinite ground plane a Find the electric field at any location x y z in front of the ground plane b Find the surface charge density on the ground plane z u Q x u Q x E2 Q z E1 x y z r2 r1 D N U O R G From Coulomb s Law E field due to a point charge is 2 3 1 2 2 2 2 3 2 2 2 2 3 2 1 2 Just to the right of the ground plane x 0 2 2 2 3 2 2 0 0 1 2 Note the subscripts 1 2 here are denoted for medium 1 and 2 whereas in the E field above the 1 2 represent the real charge 1 image 2 They have different meanings We can define the normal direction to be along the x axis and medium 2 is the conductor such that D2 0 1 1 2 2 2 3 2 2 2 2 2 3 2 2 EE140 2 MT2B Spring 2022 Dr Ray Kwok 30 pts A 1592 MHz LHCP electromagnetic wave is traveling in a non magnetic medium with a dielectric medium with r 4 Given at the origin when t 0 20 mA m The propagation direction is 0 6 0 8 Write the full expression of the corresponding electric field Simplify your answer 1010 2 3 108 66 7 66 7 0 0 6 0 8 40 53 4 0 02 3 77 377 2 E1 3 z k 4 4 3 y x out H1 out E2 in 4 3 1 5 3 77 1010 40 53 4 2 3 77 1010 40 53 4 3 0 2 26 1010 40 53 4 3 77 1010 40 53 4 EE140 MT2B Spring 2022 Dr Ray Kwok 3 35 pt A ring made of thin wire is placed in a magnetic field given by cos 100 Tesla The radius of the ring is oscillating as R 2 sin 500t meters Find the magnitude and direction of the induced current The resistivity of the thin wire is 0 3 m Use Lenz s Law to justify your answer Q10 summer 2020 y R x 2 cos 100 2 Flux is into the page 2 2 2 100 sin 100 2 cos 100 500cos 500 0 3 2 100 sin 100 1000 cos 100 cos 500 Amp 0 6 Dominating term at small t is the dR dt term At t 0 radius decreases flux decreases induced B is into the page From Lenz s Law induced current is clockwise for t 0
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