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A long solenoid with 15turns per cm has a small loop of area 2.0cm2 placed inside the solenoid normal to it's axis. If the current carried by the solenoid changes steadily from 2.0A to 4.0A in 0.1s, what is the induced emf in the loop while the current is changing ?
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Calculating the induced emf in the loop

To calculate the induced emf in the loop, we can use Faraday's law of electromagnetic induction, which states that the induced emf in a closed loop is equal to the rate of change of magnetic flux through the loop.

Calculating the magnetic flux through the loop

The magnetic flux through the loop is given by the product of the magnetic field and the area of the loop. Since the loop is inside a long solenoid with 15 turns per cm, the magnetic field is given by:

B = μ0nI

where μ0 is the permeability of free space, n is the number of turns per unit length, and I is the current in the solenoid. Substituting the given values, we get:

B = μ0 * 15 * 2 * 10^-2 * 2

B = 1.88 * 10^-4 T

The area of the loop is given as 2.0 cm^2, which is equal to 2.0 * 10^-4 m^2. Therefore, the magnetic flux through the loop is:

Φ = B * A

Φ = 1.88 * 10^-4 * 2.0 * 10^-4

Φ = 3.76 * 10^-8 Wb

Calculating the rate of change of magnetic flux

The rate of change of magnetic flux is equal to the change in magnetic flux divided by the time taken for the change. In this case, the current in the solenoid changes from 2.0A to 4.0A in 0.1s. Therefore, the change in magnetic flux is:

ΔΦ = B * A * ΔI/Δt

ΔΦ = 1.88 * 10^-4 * 2.0 * 10^-4 * (4.0 - 2.0)/0.1

ΔΦ = 7.52 * 10^-8 Wb

The time taken for the change is 0.1s. Therefore, the rate of change of magnetic flux is:

dΦ/dt = ΔΦ/Δt

dΦ/dt = 7.52 * 10^-8/0.1

dΦ/dt = 7.52 * 10^-7 V

Calculating the induced emf in the loop

Finally, the induced emf in the loop is equal to the rate of change of magnetic flux, which is:

emf = -dΦ/dt

emf = -7.52 * 10^-7 V

The negative sign indicates that the emf is induced in a direction that opposes the change in magnetic flux.
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Read the following text and answer the following questions on the basis of the same: TOROIDA toroid is a coil of insulated or enamelled wire wound on a donut-shaped form made of powdered iron. A toroid is used as an inductor in electronic circuits, especially at low frequencies where comparatively large inductances are necessary. A toroid has more inductance , for a given number of turns, than a solenoid with a core of the same material and similar size. This makes it possible to construct high-inductance coils of reasonable physical size and mass. Toroidal coils of a given inductance can carry more current than solenoidal coils of similar size, because larger-diameter wires can be used, and the total amount of wire is less, reducing the resistance . In a toroid, all the magnetic flux is contained in the core material. This is because the core has no ends from which flux might leak off. The confinement of the flux prevents external magnetic fields from affecting the behaviour of the toroid, and also prevents the magnetic field in the toroid from affecting other components in a circuit. Standard toroidal transformers typically offer a 95% efficiency, while standard laminated transformers typically offer less than a 90% rating. One of the most important differences between a toroidal transformer and a traditional laminated transformer is the absence of gaps. The leakage flux through the gaps contributes to the stray losses in the form of eddy currents (which is also expelled in the form of heat). A toroidal core doesn’t have an air gap. The core is tightly wound . The result is a stable, predictable toroidal core, free from discontinuities and holes. Audible vibration or hum in transformers is caused by vibration of the windings and core layers from the forces between the coil turns and core laminations. The toroidal transformer’s construction helps quiet this noise. In audio, or signal transmitting applications, unwarranted noise will affect sound quality, so a transformer with low audible vibration is ideal. For this reason, many sound system engineers prefer to use a toroidal transformer instead of a traditional laminated transformer.Why inductance of solenoid is more than the inductance of a solenoid having same number of turns, core of same material and similar size?

A long solenoid with 15turns per cm has a small loop of area 2.0cm2 placed inside the solenoid normal to it's axis. If the current carried by the solenoid changes steadily from 2.0A to 4.0A in 0.1s, what is the induced emf in the loop while the current is changing ?
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A long solenoid with 15turns per cm has a small loop of area 2.0cm2 placed inside the solenoid normal to it's axis. If the current carried by the solenoid changes steadily from 2.0A to 4.0A in 0.1s, what is the induced emf in the loop while the current is changing ? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A long solenoid with 15turns per cm has a small loop of area 2.0cm2 placed inside the solenoid normal to it's axis. If the current carried by the solenoid changes steadily from 2.0A to 4.0A in 0.1s, what is the induced emf in the loop while the current is changing ? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A long solenoid with 15turns per cm has a small loop of area 2.0cm2 placed inside the solenoid normal to it's axis. If the current carried by the solenoid changes steadily from 2.0A to 4.0A in 0.1s, what is the induced emf in the loop while the current is changing ?.
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