Two charged spheres 10 cm apart attract each other with a force of 3.0 x 106 N. What forceresults from each of the following changes, considered separately?a) Both charges are doubled and the distance remains the same.b) An uncharged, identical sphere is touched to one of the spheres, and then taken far away.c) The separation is increased to 30 cm.
Question
Two charged spheres 10 cm apart attract each other with a force of 3.0 x 106 N. What forceresults from each of the following changes, considered separately?a) Both charges are doubled and the distance remains the same.b) An uncharged, identical sphere is touched to one of the spheres, and then taken far away.c) The separation is increased to 30 cm.
Solution 1
a
Solution 2
a) The force between two charges is given by Coulomb's law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. If both charges are doubled, the force becomes four times as large because (2Q) * (2Q) = 4Q^2. So, the new force would be 4 * 3.0 x 10^6 N = 12.0 x 10^6 N.
b) If an uncharged, identical sphere is touched to one of the spheres, the charge will distribute evenly between the two spheres due to the principle of conservation of charge. Therefore, each sphere will have half the original charge. Using Coulomb's law again, the force will be (0.5Q) * (0.5Q) / r^2 = 0.25Q^2 / r^2. So, the new force would be 0.25 * 3.0 x 10^6 N = 0.75 x 10^6 N.
c) If the separation is increased to 30 cm (or 0.3 m), the force will decrease by a factor of (10/30)^2 = 1/9, because the force is inversely proportional to the square of the distance. So, the new force would be (1/9) * 3.0 x 10^6 N = 0.33 x 10^6 N.
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