Question

Constants Part A Two tiny spheres of mass 5.30 mg cary charges of equal magnitude, 67 0 nC. but opposite sign. They are tied to the same ceiling hook by light strings of length 0.530 m When a honzontal uniform electnc field E that is directed to the left is turned on, th spheres hang at rest with the angle 0 between the stings equal to 58 o (Figure 1) Which ball (the one on the night or the one on the left) has positive charge? the one on the left the one on the night Previous Answers Correct Part B What is the magnitude E of the feld? Express your answer with the appropriate units. Figure 1 of 1 EAN E 573 Incorrect: Try Again; 3 attempts remaining

Answer 1

a)

Answer is the one on the left Since electric field is directed towards left.

b)

at equilibrium ,from newton's second law

$\sum F_{y}=ma_{y}$

$TCos\theta_{o} -mg=0$

$T=\frac{mg}{Cos\theta_{o} }$

$\sum F_{x}=ma_{x}$

$qE-TSin\theta _{o}-F=0$

$qE-\left ( \frac{mg}{Cos\theta_{o} } \right )Sin\theta _{o}-\frac{Kq^{2}}{d^{2}}=0$

$qE-\left ( \frac{mg}{Cos\theta_{o} } \right )Sin\theta_{o} -\frac{Kq^{2}}{(LSin\theta_{o} )^{2}}=0$

$E=\frac{mg}{q }tan\theta_{o}+\frac{Kq}{4L^{2}Sin^{2}(\theta _{o})}$

here $\theta _{o}=\frac{58}{2}=29^{o}$

E=[(5.3*10^-6)(9.81)/(67*10^-9)]tan29+(9*10⁹)(67*10^-9)/4*0.53²*(sin29)²

E=2713.45 N/C