Two small metallic spheres, each of mass m 0.35 g, are suspended as pendulums by

Question

Two small metallic spheres, each of mass m 0.35 g, are suspended as pendulums by light strings from a common point as shown in the figure below. The spheres are given the same electric charge, and it Is found that they come to equilibrium when each string Is at an angle of 0 5.2 degree with the vertical. 1f each string has length L = 26.0 cm, what Is the magnitude of the charge on each sphere? [ ]nC A small object of mass 3.70 g and charge -16.4 Mu C is suspended motionless above the ground when immersed in a uniform electric field perpendicular to the ground. What are the magnitude and direction of the electric field? magnitude ___________ N/C direction [ ]

Explanation / Answer

1.

From the above diagram,

Tx = Tsin5.2 and Ty = Tcos5.2

Applying Newton’s second law along X axis,

Tsin5.2 = Fe -----------------(1)

Applying Newton’s second law along Y axis,

Tcos5.2 = mg ------------------(2)

Dividing (1) by (2)

tan5.2 = Fe/mg

Fe = mgtan5.2

kq2/r2 = mgtan5.2

but r= 2* L*sin5.2 =2*0.26*sin5.2

Plugging all given values,

(9*10^9*q2)/(2*0.26*sin5.2)2 = 0.35*10^-3kg*9.8m/s2*tan5.2         =>    q= 8.8*10-9 C

2.

Use equation eE=mg

E= mg/e = (3.7*10^-3*9.8)/(16.4*10^-6) = 2211 N/C

Direction is downward since charge in –ve

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