Test: Solenoid - NEET 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

Solenoid: A cylindrical coil of many tightly wound turns of insulated wire with a general diameter of the coil smaller than its length is called a solenoid.

• A magnetic field is produced around and within the solenoid.
• The magnetic field within the solenoid is uniform and parallel to the axis of the solenoid.

The strength of the magnetic field in a solenoid is given by:-

Where, N = number of turns, 
l = length of the solenoid,  
l = current in the solenoid and
μ_o = absolute permeability of air or vacuum.
The magnetic field inside a solenoid is uniform. So option 2 is correct.

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

Solenoid and Toroid:

• A solenoid is a coil of wire designed to create a uniform magnetic field inside when electric current flows through it.
• The magnetic field inside the solenoid is given by the formula,
  B = μ₀nI
  Where:
  • B is the magnetic field inside the solenoid,
  • (μ₀) is the permeability of free space (4π×10⁻⁷T m/A),
  • n is the number of turns per unit length,
  • I is the current flowing through the solenoid.
• A toroid is a solenoid bent into the shape of a doughnut or a circular ring.
• The magnetic field inside a tightly wound toroid is confined to the interior of the coil and is given by the formula,
  
  Where:
  • B is the magnetic field inside the toroid,
  • N is the total number of turns,
  • I is the current,
  • r is the average radius of the toroid.
• The magnetic field remains confined within the tube and follows circular paths along the axis of the toroid.

Calculation:

Given,

Current, (I) = Constant electric current
Number of turns, (N)
Average radius of the toroid, (r)

The magnetic field inside the toroid is given by,

⇒ The magnetic field is inversely proportional to the radius (r). As (r) decreases, the magnetic field increases.

The magnetic field inside the toroid remains the same.

∴ The correct option is C.

A solenoid consists of a helical winding of wire on a cylinder, usually circular in cross-section.
There can be hundreds or thousands of closely spaced turns, each of which can be regarded as a circular loop.
Magnetic field due to solenoid B = μ₀nl
μ₀ = Permeability of free space
n = no. of windings per unit length
I = current.

The direction of the field inside the solenoid is parallel to the axis, obtained by the right-hand thumb rule.
The direction of the field is shown in the figure.
If a charged particle (q) is projected with uniform velocity along the axis of the solenoid then the force on the electron

Here, q = charge of the particle
 = velocity vector of the electron
 = magnetic field
θ = angle between 
Now, when the particle (here electron) is projected along the axis of the solenoid the angle θ = 0° or 180° (as shown)

∴ F = qvB sin0 or qvB sin180
∴ F = 0
Hence, the electron will continue to move with uniform velocity.
So, the correct answer is option (b).

According to Maxwell's equations, a varying electric field generates a magnetic field. This principle is fundamental to electromagnetism and is described by Faraday's Law of Induction and Ampère's Law with Maxwell's correction.

In a current-carrying conductor:

1. The movement of charges (current) creates an electric field.
2. A varying electric field generates a magnetic field around the conductor as described by Ampère’s Law.

Why other options are incorrect:

1. B: Potential gradient:

   • A potential gradient is related to the electric field itself, not the generation of a magnetic field.

2. C: Resistance:

   • Resistance is a property of the material and is not generated by a varying electric field.

3. D: Current:

   • Current is the movement of charges due to an existing electric field, not a result of the varying electric field.

The magnetic field B inside a long solenoid is given by the formula:
⇒ B = μ₀ni
Now i → 2i
And
n → n/2

∴ The new magnetic field remains the same as the original magnetic field B

       
Since the force (Lorentz force ∵ F = -e(V × B) on the electron due to the magnetic field is zero.
So it will move along the axis with uniform velocity.

• A cylindrical coil of many tightly wound turns of insulated wire with generally diameter of the coil smaller than its length is called a solenoid.
• A magnetic field is produced around and within the solenoid. The magnetic field within the solenoid is uniform and parallel to the axis of the solenoid.
• Strength of the magnetic field in a solenoid is given by -

Where,
N = number of turns, 
l = length of the solenoid,  
l = current in the solenoid
μ_o = absolute permeability of air or vacuum.
Now
we can see that the magnetic field inside the solenoid is 

And for unit length  (l = 1) the above equation can be modified as
B = μ₀NI
Hence option C is correct among all