Two small spheres, each of mass 2.00 g, are suspended from the ceiling by string

Question

Two small spheres, each of mass 2.00 g, are suspended from the ceiling by strings each 10.0 cm long [see the figure]. A uniform electric field E is applied in the +x-direction. The charges on the spheres are -5.00 times 10^-8 C and+5.00 times 10^-8 C. If the spheres are in equilibrium each at an angle of 10.0 degree to the vertical, what is the magnitude of the electric field? 60 6.24j N 76 (a) 2.61 times 10^5 i N/C: (b) -4.17 times 10^-14i N 94. 1.22 times 10^-3 m 116. 7.46 times 10^5 N/C: 45.0 degree (I) 1.00 times 10^3 N/C (II) 4.42 times 10^5 N/C

Explanation / Answer

ii) m = 2 g = 2 x 10^-3 kg ; l = 10 cm = 0.1 m ;

q = -5 x 10^-8 C ; theta = 10 deg

Let T be the tension in the string, F1 = k q^2/d^2 ; F2 = q E

forces along x:

T sin(theta) = F2 - F1 (1)

along y:

T cos(theta) = mg (2)

1 / 2 gives us:

tan(theta) = (F2 - F1)/mg

F2 = mg tan(theta) + F1

q E = mg tan(theta) + k q^2/d^2

d = 2 L sin(theta)

E = mg tan(theta)/q + k q/(2 L sin(theta))^2 = 4.42 x 10^5 N/C

Hence,E = 4.42 x 10^5 N/C

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