Question

Two particles are separated by 0.38 m and have charges of -6.25 x 10^(-9) C and 2.91 x 10^(-9) C. Use Coulomb's law to predict the force between the particles if the distance is doubled. The equation for Coulomb's law is Fe = kq₁q₂/r², and the constant, k, equals 9.00 x 10^9 Nm²/C².

A. -2.83 x 10^(-7) N
B. 2.83 x 10^(-7) N
C. -1.13 x 10^(-6) N
D. 1.13 x 10^(-6) N

Answer 1

The force between the two particles is initially -2.83 x 10^(-7) N. When the distance is doubled, the force is reduced to -7.075 x 10^(-8) N.

Step-by-step explanation:

According to Coulomb's law, the force between two charges is directly proportional to the products of their charges and inversely proportional to the square of the distance between them. Given a distance of 0.38 m and charges of -6.25 x 10^(-9) C and 2.91 x 10^(-9) C, we can calculate the initial force using the equation Fe = kq₁q₂/r².

Substituting the given values, we have Fe = (9.00 x 10^9 Nm²/C²)(-6.25 x 10^(-9) C)(2.91 x 10^(-9) C)/(0.38 m)² = -2.83 x 10^(-7) N.

When the distance is doubled to 0.76 m, we can use the inverse square law to predict the new force. Since the distance is doubled, the force should be reduced by a factor of 1/4. Therefore, the force between the particles when the distance is doubled is (-2.83 x 10^(-7) N) x (1/4) = -7.075 x 10^(-8) N.

Therefore, the correct answer is A. -2.83 x 10^(-7) N.