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Chapter 26: Q. 42 (page 739)

Use the on-axis potential of a charged disk from Chapter 25 to find the on-axis electric field of a charged disk

Short Answer

Expert verified

The electric field of charged disk isE(z)=-Q2蟺鈭�0R2zR2+z2-1

Step by step solution

01

Given information

We need to find the on-axis electric field of a charged disk

02

Simplify

The potential on the axis of a disk with charge Qand radius Rat distance zfrom it is given as

V(z)=Q2蟺鈭�0R2R2+z2-z.

The formula for electric field is

E=-dVdr,

Where ris the direction in which we're investigating the electric field. We have to take the negative of the derivative of the first expression with respect to z. It is given as

E=-dVdz=-Q2蟺鈭�0R2ddzR2+z2-z

If we perform the calculation correctly we get

E(z)=-Q2蟺鈭�0R2zR2+z2-1

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