Test: Solenoid & Toroid - JEE MCQ

we can say that any two current carrying conductors when placed near each other, will exert a magnetic force on each other.

Consider the system shown in the figure above. Here, we have two parallel current carrying conductors, separated by a distance ‘d’, such that one of the conductors is carrying a current I1 and the other is carrying I2, as shown in the figure. From the knowledge gained before, we can say that the conductor 2 experiences the same magnetic field at every point along its length due to the conductor 1. The direction of magnetic force is indicated in the figure and is found using the right-hand thumb rule. The direction of the magnetic field, as we can see, is downwards due to the first conductor.

Lenz’s law is used for determining the direction of induced current.

Lenz’s law of electromagnetic induction states that the direction of induced current in a given magnetic field is such that it opposes the induced change by changing the magnetic field.

Following is the formula of Lenz’s law:

ϵ=−N (∂ϕ_B/∂t)

Where,

• ε is the induced emf

• ∂Φ_B is the change in magnetic flux

• N is the number of turns in the coil

Lenz’s law finds application in electromagnetic braking and in electric generators

The magnetic field is only confined inside the body of a toroid in the form of concentric magnetic lines of force. For any point inside the empty space surrounded by toroid and outside the toroid, the magnetic field B is zero because the net current enclosed in these spaces is zero. Thus, the magnetic moment of the toroid is zero.

We know, Magnetic field of solenoid,
= μonI
=4πx10^-7x300x5
=4πx15x10^-5
=6πx10^-9
=18.89x10^-9
≈1.9x10^-3T

For a toroidal solenoid, B=μ0nI 
Where, B is the magnetic field, μ0 is the permeability of free space, n is the number of coils in the solenoid per length (like 2 turns per millimetre, let's say), and I is the electric current.
i.e. It does not depend upon its radius.

In a current-carrying conductor, by varying the electric current, the magnetic field is generated. The direction of the magnetic field generated will be perpendicular to the conductor.
The direction of the magnetic field can be determined as wrapping the right-hand fingers around the wire and the direction of the current is indicated by the thumb.
Ampere’s law is used for determining the magnetic field of a long conductor:
B=μ0I/2πr
Where,

• I is the current in Amperes

• r is the radial distance in metres

• B is the magnetic field in Tesla

It is true only for an infinitely long solenoid.
Magnetic field at any point is the summation of magnetic fields produced by each turn of the wire of the solenoid.
Now imagine a solenoid in front of you stretching to infinity on both the sides, say from left to right. An infinitely long solenoid has no ends and the field everywhere inside it is the same and let its intensity be E. Now cut the solenoid at a point in front of you and throw (!) the half away. You now have in front of you, an end of the remaining half. The field at this end is now due to half the total turns and hence it is E/2.
 

A toroid is shaped like a solenoid bent into a circular shape such as to close itself into a loop-like structure. The toroid is a hollow circular ring, as can be seen in the image shown below, with a large number of turns of enamelled wire, closely wound with negligible spacing between any two turns.

The magnetic field inside and outside the toroid is zero. The magnetic field inside the toroid, along the circular turn, is constant in magnitude and its direction inside the toroid is clockwise as per the right-hand thumb rule for circular loops.
The magnetic field due to a toroid can be given as,
B= μ₀NI/2πr
Where N is the number of turns of the toroid coil, I is the amount of current flowing and r is the radius of the toroid.