Q. 63

Expert-verifiedFound in: Page 712

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

a. Find an algebraic expression for the electric field strength at the surface of a charged sphere in terms of the sphere’s potential and radius .

b. What is the electric field strength at the surface of a -diameter marble charged to ?

a.

b.

__Given__ :

a. Electric field strength :

The sphere’s potential : and

Radius : R.

b. Diameter of the marble :

Charged to :

__Theory used__ :

**Gauss' Law** tells us that the electric field outside the sphere is the same as that from a point charge. This implies that outside the sphere the potential also looks like the potential from a point charge.

a. Consider the potential and field at the sphere's surface as those of a point charge with the same charge as the sphere, located in the electric sphere's center. That is, the electric field will be and the provided potential will be

We may derive a formula for the electric field strength by substituting the second expression for the first:

b. We can calculate

using the expression we discovered.

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