Question

The force exerted by an electric charge at the origin on a charged particle at a point (x, y, z) with position vector r = x, y, z is F(r) = Kr/|r|3 where K is a constant. Find the work done as the particle moves along a straight line from (5, 0, 0) to (5, 3, 5).

Answer 1

representation of a line segment joining the points (a,b,c) & (l, min) is rlt) = 12-t).(a,b,c) +tuminy where te [0,1] therefore, from points (5,0,0) 4 (5,3,5) olt ) = (1-t),<5,0,0) + t.<5,3,5% Where te [0,1] rt) - <5(1-t),0,0) + 55+,34,5t) rit) = < 5,3t, 5+) given that F(X,Y,Z) = kr Vr3 (x+y2 + z23372 therefore, Flo(t)) = k (5)? +(93)2 + (5) mai st, st> 6) - (5 + 3442 195,{5,3t, st> K Mote that that dr = {0, 3,57 dt e work done = st.de W are will integrate from oto & because te[0,47 r1 K W-s 04279, 60, 957534,54de

W = n kl 9t+25t) To (25+24+2/3/2 W it K(34t) at = Jo 195+ 3472)312 al (68t) dt W = 1 k So last 3442 3/2 put 25+94 +² = u & (686)dt = du so & limits will chang from so to sos W rok 159 du I = 2 2 Jor 1312 So Gork done = [ So work done = k ] or w = 0.06981K