two ball A&B each have a chrge of 30micro C are apart 5cm ,what force does thecharge A exert on the charge B .At what distance will the force will be halved ?
To calculate the force between two charged objects, we can use Coulomb's law, which states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
1. Calculating the electrostatic force:
Let's assume the charges on ball A and ball B are qA = 30 micro C and qB = 30 micro C, respectively. The distance between the balls is given as 5 cm, which is equivalent to 0.05 meters.
The formula for Coulomb's law is:
F = k * (qA * qB) / r^2
where F is the force, k is the electrostatic constant (k = 9×10^9 N•m^2/C^2), qA and qB are the charges, and r is the distance between the charges.
Substituting the given values into the formula:
F = (9×10^9 N•m^2/C^2) * (30×10^-6 C * 30×10^-6 C) / (0.05 m)^2
Calculating this equation will give us the force between the charges A and B.
2. Finding the distance where the force is halved:
To find the distance at which the force is halved, we need to consider the inverse square relationship in Coulomb's law. If the force is halved, it means that the new force F' is half of the original force F.
F' = F / 2
Therefore,
k * (qA * qB) / r'^2 = F / 2
Rearranging the equation to isolate r':
r'^2 = 2 * (k * (qA * qB) / F)
Taking the square root of both sides:
r' = sqrt(2 * (k * (qA * qB) / F))
By substituting the given values and the force F, we can calculate the distance r' where the force is halved.
Note: The calculations may vary depending on the precision of the values and units used.