An infnitely long metal cylinder rotates about its symmetry axis with an angular velocity omega. the cylinder is charged. the charge density per unit volume is sigma . find the magnetic field within the cylinder.

Explanation:

Let the position of the point where magnetic field is to be determined is at distance "r" from the axis of cylinder

so here total charge lying in this region is

now magnetic field inside the cylinder is given as

here current is given as

now magnetic field is given as

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.