Question

1) Does the magnetic field outside solenoid depend on the distance from solenoid?

2) How the magnetic field inside solenoid depends on the solenoid diameter?

3) What would happen to the magnetic field inside solenoid if it is bent?

4) Can you identify North and South poles of the solenoid you studied?

5) How can you prove that the magnetic field inside solenoid is uniform?

Answer 1

a)A similar argument can be applied to the loop a to conclude that the field outside the solenoid is radially uniform or constant. This last result, which holds strictly true only near the centre of the solenoid where the field lines are parallel to its length, is important in as much as it shows that the flux density outside is practically zero since the radii of the field outside the solenoid will tend to infinity.

An intuitive argument can also be used to show that the flux density outside the solenoid is actually zero. Magnetic field lines only exist as loops, they cannot diverge from or converge to a point like electric field lines can (see Gauss's law for magnetism). The magnetic field lines follow the longitudinal path of the solenoid inside, so they must go in the opposite direction outside of the solenoid so that the lines can form a loop. However, the volume outside the solenoid is much greater than the volume inside, so the density of magnetic field lines outside is greatly reduced. Now recall that the field outside is constant. In order for the total number of field lines to be conserved, the field outside must go to zero as the solenoid gets longer.

Of course, if the solenoid is constructed as a wire spiral (as often done in practice), then it emanates an outside field the same way as a single wire, due to the current flowing overall down the length of the solenoid.

b) A solenoid is a coil of wire designed to create a strong magnetic field inside the coil. By wrapping the same wire many times around a cylinder, the magnetic field due to the wires can become quite strong. The number of turns N refers to the number of loops the solenoid has. More loops will bring about a stronger magnetic field. The formula for the field inside the solenoid is

B = m₀ I N / L

c) The magnetic field lines travel along the length of a solenoid, and if you bend the ends around, you can get the magnetic field lines to go in a circle inside a torus-shaped coil of wire. You can increase the strength of the field by putting a magnetizable material inside -- a doughnut-shaped piece of iron

d) The solenoid is a long coil containing a large number of close turns of insulated copper wire. The magnetic field produced by a current carrying solenoid is similar to the magnetic field produced by a bar magnet. The lines of magnetic force pass through the solenoid and return to the other end. If a current carrying solenoid is suspended freely, it comes to rest pointing North and South like a suspended magnetic needle. One end of the solenoid acts like a N-pole and the other end a S-pole. Since the current in each circular turn of the solenoid flows in the same direction, the magnetic field produced by each turn of the solenoid adds up, giving a strong resultant magnetic field inside the solenoid.

e)The magnetic field inside a solenoid is not that it's uniform along the length, but that it's uniform in the perpendicular directions -- that is, that the field doesn't depend on whether you're close to the axis or far from it (as long as you're inside it). It'd be easy to imagine the field would either drop off or get stronger as you move perpendicular to the axis, but it doesn't (again, for a long solenoid when you're not near the ends).