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A positive charge +Q is uniformly deposited on a spherical conducting shell of r

ID: 1837087 • Letter: A

Question

A positive charge +Q is uniformly deposited on a spherical conducting shell of radius R. Explain what a Faraday Cage is. What is the electric field (indicate magnitude and direction), inside the shell at point P? Draw equipotential surfaces through the point P'. A solid conducting sphere of radius a has a net charge +Q. What is the electric field (magnitude and direction), at a radius r > a and from this deduce the total electric flux phi through a Gaussian spherical surface (dotted). [For reference, the surface area of a sphere is A = 4pir^2.] In the figure a small, non-conducting ball of mass m = l times l0-3 kg and charge q = 2 times l0^-8 C (distributed uniformly through its volume) hangs from an insulating thread that makes an angle theta = 30 degree with a vertical, uniformly charged nonconducting sheet (shown in cross section). Consider the gravitational force on the ball and assume the sheet extends far vertically and into and out of the page. The surface charge density on the sheet produces an electric field of magnitude E = 282 V/m. Draw the direction of the electric field generated by the surface charge at the location of the ball. Show a free body diagram for the forces the charged ball experiences due to gravity, the tension from the thread, and the electric field. Calculate the horizontal distance between the ball and the sheet in equilibrium. How do capacitances combine when connected in parallel? How do capacitances combine when connected in series? Calculate the equivalent capacitance between the terminals A and B for the circuit shown in the figure.

Explanation / Answer

d)

i) if two capacitors C1 and C2 are connected in parallel,then equivalent capacitance is

Ceq=C1+C2

ii)

if two capacitors are connected in series ,then equivalent capacitance is

1/Ceq=1/C1 + 1/C2

iii)

C1 and C2 are in parallel

C12=12+5.3=17.3 uF

C12 and C3 are in seriezs ,so

1/CAB =1/17.3 +1/4.5

CAB=3.57 uF

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