Electric Field-Dimension Analysis

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The discussion focuses on determining the dimension of the constant b in the charge density function λ(x) = bx, where b is a constant and λ is a function of x. It is concluded that since the rod is a one-dimensional object, the dimension of b is C/m². Additionally, the total charge Q of the rod over its length L is calculated using the integral of λ(x), resulting in Q = (bL²)/2. The calculations and conclusions presented are confirmed as correct. This analysis effectively combines dimensional analysis with integral calculus to solve the problem.
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Homework Statement


Theres a rod and charge density ##λ## is a function of ##x##, so simply ##λ(x)=bx## and b is a constant.Find the dimension of ##b##
and Find the total charge If the length of rod is L

Homework Equations


Dimension Analysis equataion

The Attempt at a Solution


[/B]I am thinking like rod is 1 dimensional object so the dimension of b will be ##\frac {C} {m^2}## and total charge of rod will be,
## Q=\int_0^L λ(x) \, dx## and from that ##Q=\frac {bL^2} {2}##

Is this true ?
 
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You are correct.
 
Ok thanks
 
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