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Question

The linear charge density of a thin rod of length l varies with the distance x from the left-most end as λ=λ0x2(0xl). The total charge on the rod is

A
λ0l33
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B
λ0l34
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C
2λ0l23
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D
λ0l23
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Solution

The correct option is A λ0l33

Let us choose an element of length dx at a distance x from the one end as shown in the figure.

Infinitesimally small charge dq on the element :
dq=λdx

The total charge on the rod,

q=dq=x=lx=0λ0x2 dx

q=λ0[x33]x=lx=0

q=λ0l33

Hence, option (a) is the correct answer.

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