What is the magnitude of the magnetic field in h atoms electrons is the order of 1 tesla?
Answers
Answer:
Explanation:
If you naively use a Bohr-like model for the hydrogen atom, then the electron in its ground state is imagined as moving in a circular orbit of radius r and moving with a speed v. In this case you could argue the electron is moving, moving charge is current, current creates a magnetic field. Following this model you might expect the magnetic field at the centre of the loop. From classical electromagnetism the magnetic field at the centre of a loop of radius r carrying a current I is B=μ0I2r.
The question now becomes what do you use for the current. You're aware that the electron isn't a continuous charge distribution so that you have to use the following definition of current, namely current is the rate of change of charge passing you I=ΔQΔt. Now, if the electron is moving fast enough in it's orbit you can imagine it to be roughly "smeared out" along its path. The electron takes an amount of time Δt to move all the way round the orbit of length 2πr and since its speed is v, this gives Δt=2πrv and the appropriate current to use as I=ev2πr. Plugging this in gives
B=μ0ev4πr2.
But, there are a few important problems with this model, it ignores the fact that the proton and the electron acts like miniature magnets in their own right because of spin, have a look at the following reference, H.C. Ohanian, "What is spin?", Am. J. Phys. 54 (1986) 500–505.