2. Distribntion of charges Exercise 2.1: A thin non-conducting rod of finite len

Question

2. Distribntion of charges Exercise 2.1: A thin non-conducting rod of finite length L has a charge q spread uniformly along it. Find (a) the electric field and (b) the electric potential at point P located at distance y along the perpendicular bisector. Given: Find: () in P L, q and y dE dEy Solution: (a) Consider a differential element of length, dx, along the rod, that includes a differential charge, dq. In P, the charge d induces a differential electric field, dE. da The components of vector de are dE, and dE: where: LU2 Define a linear charge density, : dx L

Explanation / Answer

charge per unit length L(LAmbda) = Q/l

charge of on small part of the rod = dq = L dx

dE = Kdq/r^2

dE = KLdx/(x^2+ y^2)

dEy = dECos theta

dEy =K L y dx/(x^2 +y^2)^3/2

Ey = integration from -L/2 to L/2 of K LY dx/(x^2y^2)^3/2

Ey = K Ly x/y^2 *sqrt(x^2 +y^2) from -L/2 to +L/2

Ey = kQ/(y*sqrt((L/2)^2 + y^2)

Ey = Enet = (2/qeoy) *1/sqrt(L^2 + 4y^2)

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