A small metal sphere, carrying a net charge of q1= -2.50uC , is held in a statio

Question

A small metal sphere, carrying a net charge of q1= -2.50uC , is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q2= -7.50uC and mass 1.80g , is projected toward . When the two spheres are 0.800m apart, q2 is moving toward q1 with speed 22.0 m/s (Figure 1) . Assume that the two spheres can be treated as point charges. You can ignore the force of gravity. A) What is the speed of q2 when the spheres are 0.380m apart? B) How close does q2 get to q1?

Explanation / Answer

You can easily solve this problem from energy conservation point of view. When the two spheres are 0.800 m apart, the kinetic energy is: Ka = 0.5*m2*v2^2, where m2 = 1.80g = 0.00180kg and v2 = 22.0 m/s The potential energy of q2 in the electric field of q1 is: Pa = k*q1*q2/D, where k = 1/4*p*eo the Coulomb constant, q1 = -2.50 µC, q2 = -7.50 µC, and D = 0.800 m When the two spheres are 0.450 m apart, the kinetic energy is: Kb = 0.5*m2*V2^2, where V2 is the unknown speed of q2. The potential energy of q2 in the electric field of q1 is: Pb = k*q1*q2/d, where d = 0.450 m. Applying energy conservation, we must have: Ka+Pa = Kb+Pb The only unknown in the equation above is V2. Solve the equation to get the answer to Question 1: V2. Applying energy conservation again, we must have: Ka+Pa = Kc+Pc, where Kc =0 is the kinetic energy when q2 is closest to q1, Pc = k*q1*q2/S and S is the unknown closest distance between q1 and q2. Solve this equation you get the answer to Question 2: S.

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