Question

A time-dependent but otherwise uniform magnetic field of magnitude B0(t) is confined in a cylindrical region of radius 6.5 cm. Initially the magnetic field in the region is pointed out of the page and has a magnitude of 3.5 T, but it is decreasing at a rate of 21 G/s. Due to the changing magnetic field, an electric field will be induced in this space which causes the acceleration of charges in the region. What is the direction of acceleration of a proton placed in at the point P1, 1.5 cm from the center?

Answer 1

Explanation:

Due to changing magnetic field , there will be emf induced in the region . EMF induced will create electric field which will be circular in shape and will be uniform along its circular path

The magnitude of circular electric field can be calculated as follows

We should apply Faraday law of electro magnetic induction

e = - dФ / dt = - ∫ E dl

Here Ф = π r² B

π r² dB / dt = - ∫ E dl

π r² dB / dt = E x 2π r

E = - r / 2 x dB / dt

For a circular electric field having a particular radius , magnitude of field will be constant .

The direction of electric field will be known by lenz's law

In the given case , magnetic field is upwards and it is reducing , therefore electric field induced will be such as to prevent this change of flux.

So electric field will be anticlock-wise . Hence direction of acceleration will also be anticlock-wise on proton at 1.5 cm from the centre.