IIT JEE , AIEEE Forum - Physics , Magnetism - An electron moving in a circular orbit of radius r makes n rotations per second.

juana

What is the magnitude of magnetic field produced at the centre of the circle described?

paddy.dude

i= frequency x charge
ie i = n x e

now B at centre of a circle is given by

B = mew zero x i / 2 x r
so ans comes out to be

B = mew zero x n x e / 2 x r

dhiraj1

angular velocity =n *2pie = 2pie/t

current =e/t

b =moue not *i /r

crazynishant

An electron moving in a fixed circular path can be considered similar to a circular coil carrying current (because current arises due to flow of charges)

Now in the above mentioned case let the electron of charge ?e? moving with a angular velocity ?v?. Thus time period of revolution of electron is t= angle covered/angular velocity.
Thus t={2*(pi)}/v

Thus current flowing in the assumed coil I = charge/time period of flow of charge
Thus I=e/t or e/ [{2*(pi)}/v]
Or I =e*v/{2*(pi)}

Now the magnetic field at the center of a current carrying coil can be given as
B= uo*I/{2*r}

Thus B= uo* e*v/{4* (pi)*r}

The angular velocity is related to the mentioned angular frequency as v=2*(pi)*n

Thus B=uo*e*2*(pi)*n/{4* (pi)*r}
Or B= uo*e*n/{2*r}

Substitute values and find answer

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crazynishant

An electron moving in a fixed circular path can be considered similar to a circular coil carrying current (because current arises due to flow of charges)

Now in the above mentioned case let the electron of charge ?e? moving with a angular velocity ?v?. Thus time period of revolution of electron is t= angle covered/angular velocity.
Thus t={2*(pi)}/v

Thus current flowing in the assumed coil I = charge/time period of flow of charge
Thus I=e/t or e/ [{2*(pi)}/v]
Or I =e*v/{2*(pi)}

Now the magnetic field at the center of a current carrying coil can be given as
B= uo*I/{2*r}

Thus B= uo* e*v/{4* (pi)*r}

The angular velocity is related to the mentioned angular frequency as v=2*(pi)*n

Thus B=uo*e*2*(pi)*n/{4* (pi)*r}
Or B= uo*e*n/{2*r}

Substitute values and find answer

Rate if found useful

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