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Q .81 - Excercises And Problems

Physics For Scientists & Engineers
Found in: Page 746

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Short Answer

A thin rod of length L and total charge Q has the nonuniform CALC linear charge distribution λ(x)=λ0x/L, where x is measured from the rod's left end.

a. What isλ0 in terms of Q and L ?

b. What is the electric potential on the axis at distance d left of the rod's left end?

The constant i. comes out to be 2ni. whereas the potential at the specified point is found to be

See the step by step solution

Step by Step Solution

Step 1: Given information


A thin rod of length L and having a total charge of q, has the linear charge distributionλ(x)=λxL, where x is measured from the left-end of the rod.

Formula used:

- The electric potential at a distance r from a point charge q, is givisn as:


part(a) step 1: given information

(a) If we consider a small segment of lengthdx at a distance x from left end, then charge on this segment,


Hence, the total charge on the rod,



part(b) step 1: given information

(b) Again because of the small element of charge dq, the small potential at P,

Hence, the potential at point P, due to the entire rod is given as


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