Solenoids and Toroids MCQ Quiz - Objective Question with Answer for Solenoids and Toroids - Download Free PDF

Explanation:

Assuming long solenoid

\(\mathrm{B}=\mu_{0}\left(\frac{\mathrm{~N}}{\ell}\right) \mathrm{i} \)

\(\ell=\frac{\mu_{0} \mathrm{Ni}}{\mathrm{~B}}=\frac{\left(4 \pi \times 10^{-7}\right)(200)(0.29)}{2.9 \times 10^{-4}} \mathrm{~m} \)

∴ Lenght of the solenoid = 8π cm

Calculation:
The magnetic field inside a solenoid is given by the formula:

B = μ₀ × n × I

Where:

• μ₀ = 4π × 10^-7 weber amp^-1 m^-1 (permeability of free space)
• n = number of turns per unit length = 10 turns per cm = 10 × 10² turns/m
• I = current passing through the solenoid = 5A

Now, substituting the values into the equation:

B = (4π × 10^-7) × (10 × 10²) × 5

B = 2π × 10^-5 tesla

The magnetic induction at the axis inside the solenoid is 2π × 10^-5 tesla.

Explanation:

Assuming long solenoid

\(\mathrm{B}=\mu_{0}\left(\frac{\mathrm{~N}}{\ell}\right) \mathrm{i} \)

\(\ell=\frac{\mu_{0} \mathrm{Ni}}{\mathrm{~B}}=\frac{\left(4 \pi \times 10^{-7}\right)(200)(0.29)}{2.9 \times 10^{-4}} \mathrm{~m} \)

∴ Lenght of the solenoid = 8π cm

Calculation:

Since period of a revolving charge is \(\frac{2 \pi \mathrm{~m}}{\mathrm{qB}}\)

Where B = magnetic field

due to a solenoid = µ₀ nI 

∴ \(\mathrm{T}=\frac{2 \pi \mathrm{~m}}{\mathrm{q}\left(\mu_{0} \mathrm{nI}\right)}\)

\(75 \times 10^{-9}=\frac{(2 \pi)\left(9 \times 10^{-31}\right)}{1.6 \times 10^{-19} \times 4 \pi \times 10^{-7} \times \mathrm{n} \times 1.5}\)

∴ N = 250 

Given:

Number of turns, n = 100

Radius, r = 0.01 m

Resistance, R = 10π² Ω

Concept and Explanation:

From Faraday's Law, induced emf is:

ε = −N (dϕ / dt)

Since ε = IR and I = Δq / Δt, we get:

ε / R = −N / R × (dϕ / dt) ⇒ ΔI = −N / R × (dϕ / dt)

So, Δq = −[N / R × (Δϕ / Δt)] × Δt

The negative sign indicates that the induced emf opposes the change in magnetic flux (Lenz’s Law).

Substitute into the final formula:

Δq = (μ₀ × n × π × r²) / R

Putting values:

Δq = [4π × 10⁻⁷ × 100 × 4 × π × (0.01)²] / (10π²)

Δq = 32 μC

CONCEPT:

• 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:-

\(B=\frac{{{\mu }_{0}}NI}{l}\)

Where, N = number of turns, l = length of the solenoid,  l = current in the solenoid and μo = absolute permeability of air or vacuum.

EXPLANATION:​

• The magnetic field inside a solenoid is uniform. So option 2 is correct.

CONCEPT:

• A solenoid is an instrument that consists of copper coiling over a cylinder designed to create a strong magnetic field inside the coil because of the flow of current through the coil.
• By wrapping the same wire many times around a cylinder, the magnetic field due to the flow of current can become quite strong.
• Hence we can say that the strength of the magnetic field will change as a current through coil or number of turn’s changes.
• Magnetic field strength is independent of the diameter of the cylinder of a solenoid.
• The strength of the magnetic field in a solenoid will be directly proportional to the number of turns and amount of current flowing through a wire and will be inversely proportional to its length.
• Thus it is given by \(B = \frac{{{μ _0}NI}}{l}\)

Where N = number of turns and I = current, l = length of the solenoid

• Magnetic field due to the solenoid is given by

• As μ_o and current (I) is constant, therefore 

\(\Rightarrow \;B \propto \frac{N}{L}\;\)

\( \Rightarrow \;\frac{{{B_1}}}{{{B_2}}}\; = \;\frac{{{N_1}}}{{{N_2}}} \times \frac{{{L_2}}}{{{L_1}}}\; = \;\frac{N}{{4N}} \times \frac{{2l}}{L}\; = \;\frac{1}{2}\)

Concept:

• 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 -

\(B=\frac{{{\mu }_{0}}NI}{l}\)

Where,

N = number of turns, 

l = length of the solenoid,  

l = current in the solenoid

μo = absolute permeability of air or vacuum.

Explanation:

From the above explanation, we can see that the magnetic field inside the solenoid is 

\(B=\frac{{{\mu }_{0}}NI}{l}\)

And for unit length  (l = 1) the above equation can be modified as

\(B={{{\mu }_{0}}NI}\)

Hence option 3 is correct among all

CONCEPT:

• An electromagnet is a type of magnet in which the magnetic field is produced by an electric current.
• The magnetic field disappears when the current is turned off.

EXPLANATION:

• When a soft iron core is inserted inside the solenoid then the strength of the magnetic field becomes very large because the iron core gets magnetized by induction.
• The soft iron core helps in concentrating the magnetic lines of forces through the solenoid so that the magnetic field is almost uniform at the end face of the core.
• Hence, the strength of the magnetic field increases when a soft iron core is inserted inside a solenoid. Therefore, option 1 is correct.

• The strength of an electromagnet can be increased by increasing the number of turns of wire around the iron core and by increasing the current or voltage.

CONCEPT:

• A solenoid is an instrument that consists of copper coiling over a cylinder designed to create a strong magnetic field inside the coil because of the flow of current through the coil.
  • By wrapping the same wire many times around a cylinder, the magnetic field due to the flow of current can become quite strong.
  • Hence we can say that the strength of the magnetic field will change as a current through coil or number of turns changes.
  • Magnetic field strength is independent of the diameter of the cylinder of a solenoid.
• The strength of the magnetic field in a solenoid will be directly proportional to the number of turns and amount of current flowing through a wire and will be inversely proportional to its length and it is given as

\(\Rightarrow B = \frac{{{μ _0}NI}}{l}\)

Where N = number of turns and I = current, l = length of the solenoid

EXPLANATION:

• Inside a long current carrying straight solenoid, magnetic field lines are straight and parallel.
• The strength of parallel magnetic field lines indicates that the magnetic field is uniform everywhere inside a long solenoid.​ Therefore option 2 is correct.

CONCEPT:

• Solenoid: A type of electromagnet that generates a controlled magnetic field through a coil wound into a tightly packed helix.
  • The uniform magnetic field is produced when an electric current is passed through it.
• The magnetic field inside a solenoid is proportional to the applied current and the number of turns per unit length.
• The magnetic field inside a solenoid does not depend on the radius of the solenoid.
• The field inside is constant.

B = μ0 N i

where N is no. of turns per unit length, i is current in the solenoid and μ0 is the permeability of free space.

EXPLANATION:

The field inside a solenoid is given by:

B = μ0 N i

• Here N is the number of turns per unit length. So change in length will change the value of N.
• So The magnetic field inside a solenoid depends on the applied current and the number of turns, and the length of solenoid.
• The magnetic field inside a solenoid does not depend on the radius of it.
• Hence the correct answer is option 2.

Concept:

Solenoid:

• The solenoid is a type of electromagnet, the purpose of which is to generate a controlled magnetic field through a coil wound into a tightly packed helix.
• The magnetic field is formed around the coil when an electric current passes through it and draws the plunger in.

• The magnetic field at the center of the solenoid, B = μ₀ nI, where, n = number of turns per unit length, I = current 

Explanation:

• The magnetic field inside a long straight solenoid-carrying current is the same at all points.
• It is because the magnetic field in the solenoid is constant because the lines are completely parallel to each other.

Concept:

• Electromagnets are the kind of magnet where the wire is wrapped around an iron core
• A solenoid is a device that produces a uniform magnetic field inside it.

• The magnetic field at any point beyond the solenoid is very thin.
• The magnetic field inside the solenoid is parallel to its axis at all times.
• The magnetic field produced by a solenoid can be defined using the Law of the Ampere, B = μ₀nI, where, n = number of turns per unit length, I = current flowing

​​Explanation:

• When a soft iron piece is introduced inside the solenoid, this iron core is magnetized thereby increasing the magnetic field inside a solenoid.
• Therefore, a soft iron core inserted inside a solenoid increases the strength of the magnetic field.

Hence, the correct option is 2.

CONCEPT:

• An electromagnet is a type of magnet in which the magnetic field is produced by an electric current.
• The magnetic field disappears when the current is turned off.

EXPLANATION:

• When a soft iron core is inserted inside the solenoid then the strength of the magnetic field becomes very large because the iron core gets magnetized by induction.
• The soft iron core helps in concentrating the magnetic lines of forces through the solenoid so that the magnetic field is almost uniform at the end face of the core.
• Hence, the strength of the magnetic field increases when a soft iron core is inserted inside a solenoid.
• This increases the inductance of the solenoid. So, the inductive reactance of the solenoid increases.
• Consequently, a large fraction of the applied AC voltage appears across the solenoid. As a result of this, there is less voltage across the bulb and the brightness of the bulb decreases. Therefore, option 2 is correct.

• The strength of an electromagnet can be increased by increasing the number of turns of wire around the iron core and by increasing the current or voltage.

The correct answer is same at every point.

Key Points

Concept:

• A solenoid is an instrument that consists of copper coiling over a cylinder designed to create a strong magnetic field inside the coil because of the flow of current through the coil.
  • By wrapping the same wire many times around a cylinder, the magnetic field due to the flow of current can become quite strong.
  • Hence we can say that the strength of the magnetic field will change as a current through coil or number of turns changes.
  • Magnetic field strength is independent of the diameter of the cylinder of a solenoid.
• The strength of the magnetic field in a solenoid will be directly proportional to the number of turns and amount of current flowing through a wire and will be inversely proportional to its length and it is given as

\(\Rightarrow B = \frac{{{μ _0}NI}}{l}\)

Where N = number of turns and I = current, l = length of the solenoid

Explanation:

• Inside a long current carrying a straight solenoid, magnetic field lines are straight and parallel.
• The strength of parallel magnetic field lines indicates that the magnetic field is uniform everywhere inside a long solenoid.​
• i.e. The strength of the magnetic field inside a long current-carrying solenoid is uniform everywhere.