A time-dependent but otherwise uniform magnetic field of magnitude Bo(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 29.5 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.

Required:
What is the direction of acceleration of a proton placed in at the point 1.5 cm from the center?

The acceleration is  

Explanation:

     From the question we are told that

        The radius of the cylinder is

         The magnitude of the magnetic field is  

         The rate of decrease is  

        The distance from the center is

Faraday's law of  induction states mathematically that

Where is the induced emf

            E is the magnitude of  the  electric field

            i the change in length

          is the change in magnetic flux which is mathematically represented as

substituting this into the above equation

Where l is the circumference of the circular loop formed in the cylinder  which is mathematically represented as

And A is the area of the circular loop formed which is mathematically represented as

    So

Substituting value

Generally acceleration is mathematically represented as

Now F is the electric force which is mathematically represented as

    Substituting this into the question

Where q is the  charge on the proton with a constant value of  

     and  m is the mass of the proton with a constant value of

Substituting values

b.

explanation: