Given a continuous charge distribution consisting of: a line charge of length L

Question

Given a continuous charge distribution consisting of: a line charge of length L with linear charge density X a semicircular disc of radius R with surface charge density charge distribution is placed along the x-axis as shown in the The linear charge density is uniform, where A is a constant, and the surface charge density varies as is a constant Assume the potential of this distribution is zero at infinity, for each charge distribution answer the following questions: State the coordinate system used and w rite the expression in terms of coordinates chosen for the charge element and distance from charge element to field point Coordinate system line charge Coordinate system disk of charge -DRAW Determine the total charge of the charge distribution in terms of the appropriate variables. Determine units of the charge density constants Determine an expression for the absolute potential due to this charge distribution at a field point, along the z-axis Determine an expression for the z-component of the TOTAL Field due to the line-disk charge distribution at a field point. along the x-axis

Explanation / Answer

a) Coordinate system

=> (r , r*cos(theta) , r * sin(phi))

b) Total charge = lambda * (pi * r) + (lambda * L)

c)    Absolute potential = k * [lambda * (pi * r) + (lambda * L)]/(2r + L)

d)     z component of total electric field = k * [lambda * (pi * r) + (lambda * L)] * cos(phi)/(2r + L)

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