4. Two charged metal spheres Separated by 20 cm. attract each other with a 12 N resulting force when the charge on each sphere is reduced by half.(7.2) (a) 3 N (b) 6N (c) 24 N (d) 48 N

The force between two charged objects is given by Coulomb's Law:<br /><br />F = k * (q1 * q2) / r^2<br /><br />Where:<br /><br />* F is the force<br />* k is Coulomb's constant<br />* q1 and q2 are the charges<br />* r is the distance between the charges<br /><br />In this problem, the distance remains constant, so we can focus on the relationship between the force and the charges. If the charge on *each* sphere is reduced by half, the new charges become q1/2 and q2/2. Let's call the new force F'.<br /><br />F' = k * (q1/2 * q2/2) / r^2<br />F' = k * (q1 * q2) / (4 * r^2)<br />F' = (1/4) * k * (q1 * q2) / r^2<br /><br />Notice that k * (q1 * q2) / r^2 is the original force, F. Therefore:<br /><br />F' = (1/4) * F<br />F' = (1/4) * 12 N<br />F' = 3 N<br /><br />So the answer is (a) 3 N.<br />