Question

Challenge Yourself PRACTICE EXERCISE 4.12 Given that E = (3x² + v) a, + xa, kV/m, find the work done in moving a -2 uc charge from (0.5.0) to (2, -1.0) by taking the path (a) (0,5, 0) -> (2, 5,0) -→ (2.-1.0) (b) y = 5 -- 3x Answer: (a) 12 m), (b) 12 m).

Answer 1

PRACTICE EXERCISE 4.12 Given E= (3x+y) ax+ Xay kolm charge a= -24c We have work done by the Potential "V" in moving a charge "" as W=QV. so first we need to find the Potential "V" in each case. Also Potential 'v' is given by. v=-Se.de where t is the Electric field

a) Given Path is (0,5,0) > (2,5,0)-> (2,-1,0). de=dxax+dyay+dzaz. Therefore - Se.de = - (3274) dx + xe dy). (since ax ax = 1 2 and ay. ay=1J also Ax.ay = Qy.az-az.ax=0 on providing integration to lach variable (dre, dy, separately. V = -1 (3ery) dx + Jedy (2=0 y = 5

Note; when a vary from o to 2; we have to put y as 5; because y value is constant (not varyng). during that case. Similiary when y vary from 5 to 1; we have to treat & as 2. }

v=-{3(40)45(2-0)+ 2 (-1-6)} =-{8+10-12} v=-6ku Thur Work done (w) will be W=Qv = (-2x10-6x (-6x103) W = 12x10-3j W = 12 mj

L 6) Griven Path is Y = 5-3x. We have - SE.dl = -(((32&ty) dx+xdy) V=-{ $(3874) dx + Jedy} here since both x and y are varyng in each case we are putting "y" in the first integral part in terms ofx, il y = 5-3x. Similiarly x in the second integral part as X= 5- therefore; U = - 45 (3275-3x) dx + ((s = y) dy} where a vary from o to 2 and y vary from 5 to 1.

XO - - ocenen sadei Deputy +40(8)*5 (23-34): 32 (973 --{8+5 (2.) 3 (4-6) +5 (1-5) (1-25) =(310-63(-)-$ (24)) - = -(12-10+4) u=-(6) ku

Thur v=-bleu : work done (W) is W=Qu = (2x 10-6) (-6x103) W = 12x10-3, W = 12 mj (1 ) thus both case "a and b" are proved
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