Three point charges are located at the vertices of a right-angled triangle in the -plane
PHYSICS · Subjective · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
Three point charges are located at the vertices of a right-angled triangle in the xy-plane. A charge q is placed at the origin O(0,0,0), a charge Q at A(a,0,0) on the positive x-axis, and a charge Q at B(0,b,0) on the positive y-axis.
(i) Derive an expression for the displacement vector from Q at A to q at O and the corresponding unit vector.
(ii) Derive a similar expression for the displacement vector from Q at B to q at O and its unit vector.
(iii) Hence obtain the net electrostatic force on the charge q at the origin in terms of k,q,Q,a, and b, expressing your answer in i^ and j^ components.
(iv) Show that when a=b, the net force on q is directed along the line y=x and state whether the interaction is attractive or repulsive for (a) qQ>0 and (b) qQ<0.