An electron is released from rest at a perpendicular distance of 9.1 cm from a line of charge on a very long nonconducting rod. That charge is uniformly distributed, with 7.8 ìC per meter. What is the magnitude of the electron's initial acceleration?
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A ball with a mass of 4·kg is moving in a vertical circle at the end of a 0.9·m long rope. When the ball is at the top of the circle, it is going 7·m/s. What is the tension in the rope? (Again...don't need the answer...just the formula on how to find tension...already understand net force and centripetal acceleration...any help)??
To find the magnitude of the electron's initial acceleration, we can use Coulomb's law and the principles of electrostatics.
Coulomb's law states that the force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Mathematically, it can be expressed as:
F = k * (q1 * q2) / r^2
Where F is the force, k is the electrostatic constant (approximately equal to 9 × 10^9 N * m^2 / C^2), q1 and q2 are the charges, and r is the distance between the charges.
In this case, the electron is attracted towards the line of charge on the rod. Therefore, the force acting on the electron is given by Coulomb's law with the charge of the electron (qe) and the charge on the rod (qr):
F = k * (qe * qr) / r^2
Since the electron is released from rest, the force acting on it is equal to its mass (m) multiplied by its acceleration (a):
F = m * a
By equating these two equations, we can find the magnitude of the electron's initial acceleration (a):
a = (k * (qe * qr)) / (m * r^2)
Now we can substitute the given values into the equation to find the answer.
Given:
Charge per meter, qr = 7.8 μC/m = 7.8 × 10^-6 C/m
Distance from the line of charge, r = 9.1 cm = 0.091 m
Charge of an electron, qe = -1.6 × 10^-19 C (negative since it is attracted towards the line of charge)
Mass of an electron, m = 9.1 × 10^-31 kg
Plugging in these values:
a = (9 × 10^9 N * m^2 / C^2) * ((-1.6 × 10^-19 C) * (7.8 × 10^-6 C/m)) / ((9.1 × 10^-31 kg) * (0.091 m)^2)
Simplifying the equation, we can calculate the magnitude of the electron's initial acceleration.