EE140 MT1 Spring 2021 Dr Ray Kwok A thin wire carrying a positive and uniform linear charge density is bent into a quarter circle with a radius R as shown in the figure a Find the electric field vector at a point 0 0 z b Find the electric potential at the same location using y R x 1 z EE140 MT1 Spring 2021 Dr Ray Kwok A thin wire carrying a positive and uniform linear charge density is bent into a quarter circle with a radius R as shown in the figure a Find the electric field vector at a point 0 0 z b Find the electric potential at the same location using 1 2 3 y 2 2 2 2 2 constant 2 3 2 3 by symmetry R dq x y 0 x r 0 0 z z dE 3 2 3 3 2 2 2 2 3 2 2 2 2 Why to z Can it be to z Why dz Can it be dx dy 2 2 3 2 1 2 3 2 1 2 1 2 2 1 2 2 2 2 2 Check with direct integral 2 2 2 2 2 2 0 2 0 2 0 EE140 2 MT1 Spring 2021 Dr Ray Kwok The electric field in front of a thin charged circular disc at a distance z away from the center is given by from lecture homework and quiz problems 1 2 2 2 Use this result to find the magnitude of the electric field at the tip of a right circular cone has a base radius R height h and a uniform charge density as shown in the figure z h R Quiz Ring to disc Quiz Q on solid cone MT1 Spring 2021 Dr Ray Kwok The electric field in front of a thin charged circular disc at a distance z away from the center is given by from lecture homework and quiz problems 1 2 2 2 Use this result to find the magnitude of the electric field at the tip of a right circular cone has a base radius R height h and a uniform charge density as shown in the figure z h R 2 2 0 1 2 2 2 r z h 2 0 1 2 2 2 0 1 1 2 2 2 2 2 EE140 2 R EE140 MT1 Spring 2021 Dr Ray Kwok An infinitely long thin wire carrying a uniform charge density is placed in front of the grounded conductor at d s 0 and parallel to the z axis as shown a Find the electric field at any point x y z in the first quadrant You do not need to simplify your answer as long as all the variables are CLEARLY defined b Find the surface charge density induced on the xz plane i e at y 0 3 y s line charge d air Grounded conductor x EE140 MT1 Spring 2021 Dr Ray Kwok An infinitely long thin wire carrying a uniform charge density is placed in front of the grounded conductor at s d 0 and parallel to the z axis as shown a Find the electric field at any point x y z in the first quadrant You do not need to simplify your answer as long as all the variables are CLEARLY defined b Find the surface charge density induced on the xz plane i e at y 0 3 y x y z E field for an infinite wire Gauss s Law L2 L1 r1 line charge d s air Grounded conductor L3 L4 2 0 x 2 2 2 0 2 2 1 1 1 Similarly 2 3 4 2 2 2 0 2 2 2 0 2 2 2 0 1 2 3 4 As y 0 the only non zero component is the y component normal to conductor 0 2 2 2 2 2 2 2 2 2 2 2 2 Simplify call it the normal component and remember D E in air 1 1 2 2 2 2 Knowing D 0 inside the conductor 1 1 2 2 2 2 which is always negative x 0 as expected EE140 MT1 Spring 2021 Dr Ray Kwok 4 A long dielectric cylinder of radius a r1 2 is carrying a volume charge density of r It is completely enclosed by another cylinder of outer radius b r2 4 and has a uniform charge density 5 C m3 Find E r in all regions including the air region outside No plot is needed r2 4 r1 2 a b EE140 MT1 Spring 2021 Dr Ray Kwok 4 A long dielectric cylinder of radius a r1 2 is carrying a volume charge density of r It is completely enclosed by another cylinder of outer radius b r2 4 and has a uniform charge density 5 C m3 Find E r in all regions including the air region outside No plot is needed r2 4 r1 2 a b For r a 2 2 2 2 0 2 3 2 2 3 For b r a 2 2 3 5 2 2 3 5 2 2 2 4 2 3 5 2 2 8 For r b 2 2 3 5 2 2 3 5 2 2 2 2 3 5 2 2 2