Any help would be appreciated. Thanks! A charged cork hall of mass 0.75 g is sus

Question

Any help would be appreciated. Thanks!

A charged cork hall of mass 0.75 g is sus-pended on a light string in the presence of a uniform electric field as in the figure. When the electric field has an x-component of 2.18 x 10 5 N/C and a y-component of 3.35 x 10 5 N/C, the ball is in equilibrium at 32.3186degree. The acceleration of gravity is 9.8 m/s2, and the Coulomb constant is 8.99 x 10 9 N m2/C2. Find the charge on the ball. Answer in units of nC. Find the tension in the string. Answer in units of N.

Explanation / Answer

X component of electric field E = 2.18 x 10 5 N / C Y component of electric field E ' = 3.35 x 10 5 N /C Mass of the ball m = 0.75 g                             = 0.75 x 10 -3 kg Angle = 32.3186 o Length of the string L = 1.2 m Coulomb's constant K = 8.99 x 10 9 Nm 2/ C 2 let the tension in the string be T . Then T cos + E ' q = mg                     T cos = mg - E' q           --------( 1) And T sin = E q            -------( 2) Eq( 2) / Eq( 1) ==> tan = Eq / [mg - E ' q]                        mg - E ' q = Eq / tan                                        = 3.445 x 10 5 q                                  mg = 679.594 x 10 3 q from this charge of the ball q = mg / (679.594 x 10 3)                                               = 10.81x 10 -9 C                                               = 10.81 nC

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