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In an orbit of radius 0.5 A an electron revolution with frequency of 6.25×10power 15hz.then magnetic induction field at its centre is?
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Calculation of Magnetic Induction Field at the Centre of Electron Orbit


Given Information:


  • Radius of the electron orbit: 0.5 A

  • Frequency of electron revolution: 6.25 x 10^15 Hz



Formulae Used:


  • Magnetic Induction Field at the Centre of an Orbit: B = μ₀I/2r

  • Current: I = qf

  • Charge of Electron: q = 1.6 x 10^-19 C

  • Permeability of Free Space: μ₀ = 4π x 10^-7 Tm/A



Calculation:


  • Current: I = qf = (1.6 x 10^-19 C) x (6.25 x 10^15 Hz) = 1 x 10^-3 A

  • Magnetic Induction Field: B = μ₀I/2r = (4π x 10^-7 Tm/A) x (1 x 10^-3 A) / (2 x 0.5 A) = 1 x 10^-6 T



Answer:

The magnetic induction field at the centre of the electron orbit is 1 x 10^-6 T.


Explanation:

When an electron moves in a circular orbit, it produces a magnetic field due to its motion. The direction of the magnetic field is perpendicular to the plane of the orbit and is given by the right-hand rule. The strength of the magnetic field depends on the frequency of revolution and the radius of the orbit.

In this problem, we are given the radius of the electron orbit and the frequency of revolution. Using the formula for current, we can calculate the current produced by the electron in the orbit. Using the formula for magnetic induction field at the centre of an orbit, we can then calculate the magnetic induction field produced by the electron at the centre of its orbit.

It is important to note that the magnetic field produced by a single electron is very small and is usually measured in microtesla (μT) or even smaller units like nanotesla (nT) or picotesla (pT).
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In an orbit of radius 0.5 A an electron revolution with frequency of 6.25×10power 15hz.then magnetic induction field at its centre is?
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