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

Answered: 7. Calculate the work that must be done…

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Chapter1: Units, Trigonometry. And Vectors

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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

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: $k = 9 \times 10^{9} {Nm}^{2} / C^{2}$

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

$d W = Q d V$ ......(1)

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

$d V = k \frac{d Q}{R}$

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

$\begin{array}{rcl} d W & = & Q (k \frac{d Q}{R}) \\ = & \frac{k}{R} (Q d Q) \end{array}$

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

$\begin{array}{rcl} W & = & \frac{k}{R} (\frac{Q^{2}}{2}) \\ = & \frac{k Q^{2}}{2 R} \end{array}$

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

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