explai biot-savart,law.an electron with velocity 3*107ms1 describe a circular path in a uniform magnetic field of 0.2T,perpendicular to it.calculate the radius of path
The magnetic field B provides the centripetal force to keep it in a circular path.
e V B = m V^2/R
R = mV/(eB)
m and e are the electron mass and charge.
You don't need the Biot Savart Law for this question. There are plenty of good explanations of it online.
The Biot-Savart law is a fundamental principle in electromagnetism that describes the magnetic field produced by a current-carrying wire. It states that the magnetic field at a point in space due to a small section of current-carrying wire is directly proportional to the current magnitude, the length of the wire section, and the sine of the angle between the wire and the vector connecting the wire to the point in space.
To calculate the radius of the circular path that an electron takes in a uniform magnetic field, we can use the equation for the centripetal force:
F = mv^2/r
where F is the force acting on the electron, m is the mass of the electron, v is the velocity of the electron, and r is the radius of the circular path.
In this case, the force acting on the electron is the magnetic force due to the magnetic field, which can be calculated using:
F = qvB
where q is the charge of the electron and B is the magnetic field.
Since the force acting on the electron is given by both equations, we can equate them:
mv^2/r = qvB
We can solve this equation for r:
r = mv/(qB)
Given:
- Velocity of the electron, v = 3 * 10^7 m/s
- Magnetic field, B = 0.2 T
To find the radius of the circular path, we need to know the mass of the electron (m) and the charge of the electron (q). The mass of the electron is approximately 9.11 * 10^-31 kg, and the charge of the electron is approximately -1.6 * 10^-19 C.
Substituting the known values into the equation:
r = (9.11 * 10^-31 kg) * (3 * 10^7 m/s) / ((-1.6 * 10^-19 C) * (0.2 T))
r ≈ 2.269 * 10^-3 meters
Therefore, the radius of the circular path is approximately 2.269 * 10^-3 meters.