an atom is placed in a uniform magnetic induction B. such that its plane normal to the electron orbit makes an angle of 30 degrees with the magnetic induction the torque acting on the orbiting electron?
an atom is placed.....such that its plane normal to the electron orbit makes....
What electron< Orbit of what? Is some one really thinking electrons orbit a central nucleus of an atom?
Somehow, I am missing the point of all this.
To calculate the torque acting on the orbiting electron in this scenario, we need to use the formula for the torque on a current loop in a magnetic field.
Let's break down the problem step by step:
1. Find the magnetic moment (μ) of the electron's orbit:
The magnetic moment is defined as the product of the current (i) flowing through the loop and the area (A) of the loop. In this case, the loop is the electron orbit.
μ = i * A
2. Calculate the area of the loop:
The area of the loop is given by the formula: A = π * r^2, where r is the radius of the electron orbit.
3. Determine the current flowing through the loop:
The current (i) in this case is the charge (e) of the electron multiplied by the angular velocity (ω) of the electron in its orbit.
i = e * ω
4. Find the torque (τ) acting on the electron:
The torque is given by the cross product of the magnetic moment (μ) and the magnetic field (B):
τ = μ * B * sin(θ)
In this case, the angle between the electron orbit's plane and the magnetic induction is 30 degrees (θ = 30°).
Now, let's put it all together:
1. Calculate the area of the loop:
A = π * r^2
2. Determine the current flowing through the loop:
i = e * ω
3. Calculate the magnetic moment:
μ = i * A
4. Find the torque acting on the orbiting electron:
τ = μ * B * sin(θ)
Plug in the values for the charge of an electron (e), the angular velocity (ω), the radius of the electron orbit (r), and the magnetic induction (B) to get the final result.
Note: Be sure to use consistent units throughout the calculations.