7. Calculate the work that must be done on charges to bring them from infinity to charge a spherical shell of radius R to a total charge Q. 8. How many electrons should be removed from an initially uncharged spherical conductor of radius 0.300 m to produce a potential of 7.5 kV at the surface? The charge of the electron is 1.6 x 10-19 C.

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Chapter1: Units, Trigonometry. And Vectors
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7. Calculate the work that must be done on charges to bring them from infinity to charge a
spherical shell of radius R to a total charge Q.
8. How many electrons should be removed from an initially uncharged spherical conductor of
radius 0.300 m to produce a potential of 7.5 kV at the surface? The charge of the electron is 1.6
x 10-19 C.
Transcribed Image Text:7. Calculate the work that must be done on charges to bring them from infinity to charge a spherical shell of radius R to a total charge Q. 8. How many electrons should be removed from an initially uncharged spherical conductor of radius 0.300 m to produce a potential of 7.5 kV at the surface? The charge of the electron is 1.6 x 10-19 C.
Expert Solution
Step 1

Given data:

The work done on the charge is: W

The radius of the spherical shell is: R

The total charge is: Q

The Coulomb constant is: k=9×109 Nm2/C2

(7)The work done on the charge Q is given as,

dW=QdV......(1)

The potential of the sphere of dQ charge having radius R is,

dV=kdQR

Put this value of dV in the equation (1) and solve,

dW=QkdQR=kRQdQ

When we integrate dQ from limit 0 to Q then we get,

W=kRQ22=kQ22R

Thus, this is the work that must be done on the charges.

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