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1. Problem (1): A point charge of 4|C is 3cm apart from charge 1pC. Find the magnitude of the Coulomb force that one particle exerts on the other and tell if the force is attractive or repulsive.
2. Problem (2): Two like and equal charges are at a radius of 5cm and exert a force of F=9×10-3 N on each other. Find the magnitude of each charge and tell if the force is attractive or repulsive.
3. Problem (3): A point charge of 6nC charge 3nC exerted a force of 1.23×10-6. What is the magnitude of the radius?
Answers & Comments
Answer:
Problem (1): The Coulomb force can be calculated using the formula F = k * q1 * q2 / r^2, where k is the Coulomb constant (8.99 x 10^9 Nm^2/C^2), q1 is the magnitude of the first charge, q2 is the magnitude of the second charge, and r is the distance between the two charges.
Using the given values, q1 = 4 C and q2 = 1 pC (converted to C), r = 0.03 m:
F = 8.99 x 10^9 Nm^2/C^2 * 4 C * 1 C / (0.03 m)^2 = 2.40 x 10^11 N
The force is attractive since like charges repel and opposite charges attract.
Problem (2): The magnitude of the charges can be calculated using the formula F = k * q^2 / r^2, where k is the Coulomb constant, q is the magnitude of the charges, and r is the distance between the charges.
Using the given values, F = 9 x 10^-3 N and r = 0.05 m:
q^2 = F * r^2 / k = 9 x 10^-3 N * (0.05 m)^2 / (8.99 x 10^9 Nm^2/C^2) = 1.80 x 10^-12 C^2
The magnitude of each charge is q = sqrt(1.80 x 10^-12 C^2) = 1.34 x 10^-6 C
The force is attractive since like charges repel and opposite charges attract.
Problem (3): The magnitude of the radius can be calculated using the formula F = k * q1 * q2 / r^2, where k is the Coulomb constant, q1 is the magnitude of the first charge, q2 is the magnitude of the second charge, and r is the distance between the two charges.
Using the given values, q1 = 6 nC (converted to C), q2 = 3 nC (converted to C), and F = 1.23 x 10^-6 N:
r^2 = k * q1 * q2 / F = 8.99 x 10^9 Nm^2/C^2 * 6 C * 3 C / 1.23 x 10^-6 N = 5.58 x 10^16 m^2
The magnitude of the radius is r = sqrt(5.58 x 10^16 m^2) = 7.49 x 10^8 m.
Explanation:
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