A particle with a charge 7C and a mass of 20kg is traveling in a circular path around a fixed particle of charde -5C. The velocity is observed to be 3000m/sec. What is the radius of the circular path?
To determine the radius of the circular path, we can apply the principles of electrostatics and circular motion. Here's how you can solve this problem step by step:
Step 1: Identify the given values:
- Charge of the moving particle (q1) = +7 C
- Charge of the fixed particle (q2) = -5 C
- Mass of the moving particle (m) = 20 kg
- Velocity of the moving particle (v) = 3000 m/s
Step 2: Calculate the electrostatic force between the two particles:
The electrostatic force (F) between two charged particles can be found using Coulomb's law:
F = (k * |q1 * q2|) / (r^2)
In this case, |q1 * q2| = |7 C * 5 C| = 35 C^2 (taking the magnitude since the charges have different signs)
Also, the constant k in Coulomb's law is approximately 9 × 10^9 N m^2 / C^2.
Step 3: Calculate the centripetal force required for circular motion:
The centripetal force (Fc) required for an object moving in a circular path of radius (r) and velocity (v) can be calculated using the formula:
Fc = (m * v^2) / r
Step 4: Equate the electrostatic force and centripetal force:
Since the electrostatic force acting between the two particles provides the centripetal force, we can equate those two expressions:
F = * |q1 * q2|) / (r^2) = (m * v^2) / r
Step 5: Solve for radius (r):
Rearrange the equation to solve for r:
r^3 = (m * v^2 * r) / (k * |q1 *q2|)
r^3 = (m * v^2) / (k * |q1 *q2|)
r = ∛[(m * v^2) / (k * |q1 *q2|)]
Substitute the given values into the equation and calculate the result.
After solving the equation, you should find the value of the radius (r) for the circular path around the fixed particle.