Long Quantitative Questions (12 pts each) A conducting sphere has a total charge

Question

Long Quantitative Questions (12 pts each) A conducting sphere has a total charge of SuC with a radius of 4cm and is contained in thin sp shell of radius 8cm ) 10cm with a charge of -SuC. What is the electric field at a) 2cm, b) 6cm, c 6. In the circuit shown below R1-20, R2 m 1Q, R3m40, VI-SV, V2-TV, V3«SV. Find the currents each of the three resistors. Name the current with the same index as resistor it flows thre us question (1pt): lectron, a very negative guy, and his much more positive wife Mrs. Proton look o capacitor with its negatively charged plate on their left and its positively charge Using the landscape analogy we discussed in class draw the electric potential se a separate diagram draw the electric potential seen by Mrs. Proton. Label the e which person's point of view they represent. Diagrams MUST be drawn in yo sheet.

Explanation / Answer

Current through V1, upward = i1

Current through V2, upward = i2

Current through V3, downward = i3

Using kirchoff's junction law

i1 + i2 = i3

Now using kirchoff's voltage law in left loop

V1 - V2 = i1*R1 - i2*R2

5 - 7 = 2*i1 - 1*i2

i2 - 2*i1 = 2

Now using kirchoff's voltage law in right loop

V2 + V3 = i2*R2 + i3*R3

7 + 5 = 1*i2 + 4*i3

i2 + 4*i3 = 12

i1 + i2 = i3

i2 - 2*i1 = 2

Solving above three equation

i1 = 1/7 = 0.143 Amp

i2 = 16/7 = 2.286 Amp

i3 = i1 + i2 = 17/7 = 2.429 Amp

To check the solution

Now using kirchoff's voltage law in whole loop

V1 + V3 = i1*R1 + i3*R3

5 + 5 = 0.143*2 + 2.429*4

10 = 10

So our answer is correct,

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