Question

A rod is bent into a semicircle. find the electric field at its centre

Answer 1

Consider a uniformly charged thin rod bent into a semicircle of radius R.

Find the electric field generated at the origin of the coordinate system.

Charge per unit length: ? = Q/pR

Charge on slice: dq = ?Rd? (assumed positive)


Electric field generated by slice: dE = kdq/r^2=k*lamda/r *dtheta

Components of d~E : dEx = dE cos ?, dEy = -dE sin ?

Electric field from all slices added up:

Ex =0

Ey= -2klambda/r


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