A semicircular disc of radius \"R\" carries a charge \"Q\" distributed non-unifo

Question

A semicircular disc of radius "R" carries a charge "Q" distributed non-uniformly over its surface. It is centered at the origin of the x-y-z coordinate system.The disc lies in the y-x plane The surface charge density is given by a*sin(theta), where a is constant with units of coulumbs/m^2 and (theta) is measured off the y-axis. Assume the potential is zero at infinity

Determine the constant "a" in terms of "Q" and "R"

Determine the potential at a point "P" along the x-axis

Find the Electric Field along the x-axis

Explanation / Answer

density = a sin (theta)

dq = density * dA .............(1)

dA = d(theta)*(pi)*R*R/360

Putting the value of density and dA in 1 and integrating from 0 to 180

Q = (Pi)*R*R*a/180

a = 180Q/((Pi)*R*R)

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