A thin insulating rod of length lies along the -axis from to

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Electricity, Magnetism & Electromagnetism · Electrostatic fields and potential

Mathematical Methods for Physics, Ch Accumulation: integration and the techniques that make it possible

Problem

A thin insulating rod of length L=0.50 mL = 0.50\,\mathrm{m} lies along the xx-axis from x=0x=0 to x=Lx=L, carrying a linear charge density λ(x)=λ0sin⁡ ⁣(πxL),λ0=3.0×10−6 C m−1.\lambda(x) = \lambda_0 \sin\!\left(\frac{\pi x}{L}\right), \qquad \lambda_0 = 3.0\times10^{-6}\,\mathrm{C\,m^{-1}}. (a) Name the slice of the rod you would add up to find the total charge, and state the charge it carries. (b) Write the integral for the total charge QQ on the rod and evaluate it.

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