Please answer only questions d! with full explanation and consider the absolute value on x! and separate i and j components.
Please answer only questions d! with full explanation and consider the absolute value on x! and separate i and j components.
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Question
Please answer only questions d! with full explanation and consider the absolute value on x! and separate i and j components.
Transcribed Image Text:EXERCISE
Note: Your instructor will not provide a solution package for this exercise.
IA-1. Consider a finite line segment having a linear charge density λ(x)
=
10 |x| (x is
in m and is in C/m). The line segment extends to a length of L on either side of
the origin.
Hint: In setting up the integrals, break the rod into two symmetric parts.
-L
2(x)
dx
dq
(a) Consider a small element of length dx and position x. What is the charge dq of
this element? Express your answer in terms of x and dx.
(b) What is the total charge of the rod? Express your answer in terms of L.
(c) What are (i) the electric field dĒ, (ii) the electric potential dV, at P due to dq?
Express your answers in terms of x, dx and y.
(d) What are (i) the net electric field Ē, (ii) the net electric potential V, at P due to the
entire rod? Use symmetry wherever possible, and evaluate your final integrals.
Express your answers in terms of y and L.
Expert Solution
Introduction:
We are given the symmetric rod. We find the electric potential and electric field due to small charge element. We then integrate this potential or field for the entire length. Since the rod is symmetrical, the horizontal components of electric field from 2 symmetrical points cancel out.
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