[PHYS] Example Question: An isolated charged conducting sphere has a radius R = 11.0 cm. At a distance of r = 19.0 cm from the center of the sphere the electric field due to the sphere has a magnitude of E = 4.90 ✕ 104 N/C.

Example Question

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# Example Question

An isolated charged conducting sphere has a radius R = 11.0 cm. At a distance of r = 19.0 cm from the center of the sphere the electric field due to the sphere has a magnitude of E = 4.90 ✕ 104 N/C.

• What is its surface charge density (in µC/m2)?
• What is its capacitance (in pF)?
• A larger sphere of radius 23.0 cm is now added so as to be concentric with the first sphere. What is the capacitance (in pF) of the two-sphere system?

 

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# Explanation

Radius R = 11.0 cm = 0.11 m

Distance r = 19.0 cm = 0.19 m

Magnitude E = 4.9 * 104N/C

 

1) What is its surface charge density (in µC/m2)?

2) What is its capacitance (in pF)?

3) A larger sphere of radius 23.0 cm is now added so as to be concentric with the first sphere. What is the capacitance (in pF) of the two-sphere system?

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# Answer

1) 1.28

2) 12.2

3) 23.45

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