Question

Consider the figure with a symmetrical arrangement, in which ?a=?b= +7.75?C, ?c=?d= −7.75?C, and ? is positive. Calculate the magnitude of the force ? on the charge ? given that the square is 10.70 cm on a side and ?=2.75?C.

qa 90 9 9c 9d

Answer 1

Ans

The magnitude of Force F = 94.77 N

Explanation

Ans. A В 45 ?а: 7:75 с • 7.75 x 156, Q, = 7-75 дс = 7-73 xloc - 7.75 с - 7-75 x166с. a = -7.75 дс . -7.75 x 6-6 с с Fa * E 2 Fc ac са Ав: Вс - СЬ .PA = lo-7о (т о. То То т •15 11 С = -75 х/o-6 с 2. AC = BP = Г (1os 70)* + (lo-76) 2 x |о. То 15. 138 см 0-15 13 т.

O A = OB = OC = OD = 0.15132 2 = 0.07566 m Force due to due to 9B Charge is Fc and due to 2. is Fd on is FB, due to ec charge ad charge Net force along is en charge is FA charge diagonal At Fc = K 1911291 (0A)? AC (Magnitude) FAC K 121 12cl + (002

1 417Co of charge FAC Coulomb's constant 9x109 -2 N m²c 121, Iaal and lecl are magnitude 9x109 x 3.75 x 10-6 x 7.75 x 10-6 + 9x 10 x 2.75 X 106 (0.07566)? 10.07566)? 2 x 9x 109 x 2.75 x 10 x 7.75x10-6 (0.07566)? x 7.75 x 10-6 6 67.01 N. Net Force BD is along diagonal FBA Fot Fo 1901 FBD : K t K 1211981 (OB)? klal 100j?

FBD -6 = 2x9x109 x 2- 75 x 106 x 775 X lo (0.07566) ? 67. ol N are at 9. Therefore diagonals of of Square intersect at 90°. and FBD FAC Thus force angle There total force magnitude F = TIF Ac)? +(FBD) - 94.77 N V167.01° +76 7.0))? 2 IN

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