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Chapter 25: Q. 65 (page 712)

A Van de Graaff generator is a device for generating a large electric potential by building up charge on a hollow metal sphere. A typical classroom-demonstration model has a diameter of 30cm.

a. How much charge is needed on the sphere for its potential to be500,000V?

b. What is the electric field strength just outside the surface of the sphere when it is charged to 500,000V?

Short Answer

Expert verified

a. The temperature isQ=830nC

b. There is a 3.3×106N/Celectric field.

Step by step solution

01

Given information and theory used

Given :

Diameter of the classroom-demonstration model : 30cm.

a. Potential to be on the sphere : 500,000V

b. The sphere is charged to : 500,000V

Theory used :

The potential of the spherical conductor is given byV=14πε0QR

02

Calculating the charge needed and electric field strength 

a. Here R=15cmis the radius of the sphere, is the potential of the spherical conductor. This gives

Q=4πε0RV=830nCfor the charge.

b. The field is E=14πε0QR2=14πε0QR⏟V1R=VR

As a result,

E=3.3×106N/C.

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