The magnetic field within a long, straight solenoid with a circular cross section and radius r is increasing at a rate of dbdt. part a what is the rate of change of flux through a circle with radius r1 inside the solenoid, normal to the axis of the solenoid, and with center on the solenoid axis? express your answer in terms of the variables r, b, r1, and appropriate constants.

Explanation:

To calculate the rate of change of the flux we have to take into account that the magnetic flux is given by

in this case the direction of B is perpendicular to the direction of A. Hence

and A is the area of a circle:

in this case we are interested in the flux of a area of a lower radius r1. Hence

Finally, the change in the magnetic flux will be

hope this helps!!

reserve is the answer

force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach