Question

A 100.0 m rod with a diameter of 3.0mm has a charge of 1004.0C. What is the approximate electric field 2.0mm from the surface of the rod, not near either end?

A) 9.0*10¹¹ r N/C

B) - 9.0*10¹¹ r N/C

C) - 5.2*10¹³ r N/C

D) 5.2*10¹³ r N/C

The answer is D, I am not sure how they got that answer, can you please explain and show your work. Thanks in advance

Answer 1

Well, it is an interesting question....!!!

Here, we will deal with Gauss's Flux Law. It is the key to approach.

Let this Equation----------1

where    : Electric flux through the area

      : Electric charge inside the surface

      : Electric constant of the medium

But, the electric flux can be written as follows

   let this, Equation----------2

Where A : Area of the considered surface

E : Electric field

Now compare and equate the Equations 1,2

Hence the Electric field can be given as

   let us say, Equation------3

Now, Let us consider our question

rod, Diameter , Charge

Question is "Value of electric field at a distance of from the rod surface"

Now, we can consider the cylindrical area arround the rod governed by of radius or of diameter, as the  Gauss's area.

So, Now finding the area , so that the electric field on the surface of the area is the value that asked in the question

  

Substitute this in Equation-----3

     

now substitute the values for

ie)   approximately.

Here, Note that, we can not find the electric field near the each end of the rod by using the same way, because, the variation of electric field is different in that area.

Are you ok now.....Dear friend.