Fig. 19.13. Diagram showing an infinitesimal length dx at an arbitray distance a

Question

Fig. 19.13. Diagram showing an infinitesimal length dx at an arbitray distance along he rod of length L. The distance form point P to the segment is denoted as x.

a. Explain why the fraction of charge, q, on each infinitesimal length dx on the rod is given by

dq = q^tot (dx/L) where q^tot is the total charge on the rod.

b. Refer to Figure 19.13. to explain why the x-component of the electric field, dEx, at point P

Fig. 19.13. Diagram showing an infinitesimal length dx at an arbitray distance along he rod of length L. The distance form point P to the segment is denoted as x.

Explanation / Answer

linear charge density = total cahrge / total length

linear charge density = qtot/L

charge present in infinitesimal length dx = density*dx

charge present in infinitesimal length dx , q= (qtot/L)*dx

charge present in infinitesimal length dx , q= qtot*(dx/L)

electric field due to small charge = E = k*q/r^2

electric field due to infinitesimal charge = Ex = k*q/x^2

electric field due to infinitesimal charge = Ex = (k*qtot*(dx/L)x^2

electric field due to infinitesimal charge = Ex = (k*qtot/Lx^2)*dx

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