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Q. 63

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

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.

See the step by step solution

Step by Step Solution

Step 1 : Given information and theory used

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.

Step 2 : Finding an algebraic expression for the electric field strength and required electric field strength 

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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