Two small charged spheres are 5.0 cm apart. One is charged to +25 nC, the other to −15 nC. A proton is released from rest halfway between the spheres. What is the proton's speed after it has moved 1.0 cm?
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Identify the charges and distances involved. The first sphere has a charge of +25 nC and the second sphere has a charge of -15 nC. The initial distance from the proton to each sphere is 2.5 cm, and the proton moves 1.0 cm towards one of the spheres.
Calculate the electric force exerted on the proton by each sphere using Coulomb's Law, F = k \frac{|q_1 q_2|}{r^2}, where k is Coulomb's constant, q_1 and q_2 are the charges, and r is the distance between the charges.
Determine the net force on the proton by vectorially adding the forces from each sphere, considering the direction of each force (attraction or repulsion).
Use Newton's second law, F = ma, to find the acceleration of the proton, where m is the mass of the proton and a is the acceleration.
Calculate the final speed of the proton using the kinematic equation v^2 = u^2 + 2as, where u is the initial speed (0 m/s, since the proton starts from rest), a is the acceleration, and s is the displacement (1.0 cm). Convert all units to meters and kilograms as necessary.