Asteady current i flows through a wire of radius a. the current density in the wire varies with r as j = kr, where k is a constant and r is the distance from the axis of the wire. find expressions for the magnitudes of the magnetic field inside and outside the wire as a function of r. (hint: find the current through an ampèrian loop of radius r using ithru = j · da. use the following as necessary: μ0, i, a and r. do not substitute numerical values; use variables only.)a. b inside=? b. b outside=?

Explanation:

we can consider an element of radius r < a and thickness dr.  and Area of this element is

since current density is given

then , current through this element will be,

integrating on both sides between the appropriate limits,

Magnetic field can be found by using Ampere's law

for points inside the wire ( r<a)

now, consider a point at a distance 'r' from the center of wire. The appropriate Amperian loop is a circle of radius r.

by applying the Ampere's law, we can write

by symmetry will be of uniform magnitude on this loop and it's direction will be tangential to the loop.

Hence,

now using equation 1, putting the value of k,

B)

now, for points outside the wire ( r>a)

consider a point at a distance 'r' from the center of wire. The appropriate Amperian loop is a circle of radius l.

applying the Ampere's law

by symmetry will be of uniform magnitude on this loop and it's direction will be tangential to the loop. Hence

again using,equaiton 1,

the duration of a photographic flash is related to an rc time constant, which is 0.100 μs for a certain camera.

electromagnetic shielding is the practice of reducing the electromagnetic field in a space by blocking the field with barriers made of conductive or magnetic materials. shielding is typically applied to enclosures to isolate electrical devices from their surroundings, and to cables to isolate wires from the environment through which the cable runs. electromagnetic shielding that blocks radio frequency electromagnetic radiation is also known as rf shielding.

the shielding can reduce the coupling of radio waves, electromagnetic fields and electrostatic fields. a conductive enclosure used to block electrostatic fields is also known as a faraday cage. the amount of reduction depends very much upon the material used, its thickness, the size of the shielded volume and the frequency of the fields of interest and the size, shape and orientation of apertures in a shield to an incident electromagnetic

from wikipedia