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EE 140 Spring 2015 Mid Term 1 Dr Ray Kwok Name Last First 1 A rectangular coil with N turns and total resistance R length L 1 and width W 1 as shown in figure The coil moves into a uniform magnetic field B with constant velocity v Plot the induced current I2 as shown as a function of x when the coil is entering the region Clearly state the magnitude of the current I2 x x x x x x x x x x x x B x x x x x x I2 V NBvW R x x x x x x W L x x x x x x L 1 x x x x x x NBvW R x x x x x x 0 r r B da BxW d NBvW dt NBvW I2 R R N 1 x 1 L x t EE 140 Spring 2015 Mid Term 1 2 A toroid is a doughnut shaped toroidal solenoid as shown In practice it has many more turns of wire closely packed than it is in figure Use Ampere s Law and the loops shown in Figure b find B field as a function of r for N turns of wire carrying a current I What is the direction of this B field The inner radius of the toroid is a and the outer radius is b r r B d l o I enclosed I r a 0 B r a 0 a r b B 2 r o NI B o NI 2 r I 0 r b B r b 0 B field circulates in the direction shown Dr Ray Kwok EE 140 Spring 2015 Mid Term 1 Dr Ray Kwok 3 A total charge Q is deposited onto a conducting sphere with radius a which is shielded by a metal shell of inner radius b and outer radius c as shown The outer shell is grounded outside Plot E field as a function of r Clearly explain your answer What is the surface charge density at r a At r b And at r c c b a Q r a 0 E E r a 0 a r b E da Q 4 o a 2 E Q 4 o b 2 Qinside E 4 r 2 E E o Q o Q 4 o r 2 r E r b 0 a Q 4 a 2 Q r b 4 b 2 r c 0 r a b c EE 140 Spring 2015 Mid Term 1 Dr Ray Kwok 4 a A ring of charge with linear charge density and radius R is lying on the xy plane Find the electric field at a distance z above the center of the ring b Integrate this E field to find the electric potential at that point 0 0 z c Apply the E field from part a to a 2 dimensional disk Find the E field of a charged disk