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The magnetic field inside a toroidal solenoid of radius R is B. If the current through it is doubled and its radius is also doubled keeping the number of turns per unit length the same; magnetic field produced by it will be:

  • a)
    B/2

  • b)
    B/4

  • c)
    B

  • d)
    2B 

Correct answer is option 'D'. Can you explain this answer?
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The magnetic field inside a toroidal solenoid of radius R is B. If the...
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The magnetic field inside a toroidal solenoid of radius R is B. If the...
Explanation:

When a current carrying solenoid is wrapped in the shape of a toroid, the magnetic field inside the toroid is proportional to the current, number of turns, and inversely proportional to the radius of the toroid.

So, the magnetic field inside a toroidal solenoid of radius R is given by:

B = μ₀NI/2πR

Where, N is the number of turns per unit length, I is the current and μ₀ is the permeability of free space.


When the current through the solenoid is doubled, the magnetic field inside the toroid becomes:

B' = μ₀N(2I)/2πR

B' = 2(μ₀NI/2πR)

B' = 2B


When the radius of the toroid is doubled, the magnetic field inside the toroid becomes:

B" = μ₀N(I)/2π(2R)

B" = (1/2)B


Therefore, the magnetic field produced by the toroidal solenoid when the current and radius are doubled will be:

B'"/B = B'/B"

B'"/B = (2B)/((1/2)B)

B'"/B = 4


Hence, the correct answer is option D) 2B.
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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?

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.A toroid has _____ inductance, for a given number of turns, than a solenoid with a core of the same material and similar size.

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.Toroid is a

The magnetic field inside a toroidal solenoid of radius R is B. If the current through it is doubled and its radius is also doubled keeping the number of turns per unit length the same; magnetic field produced by it will be:a)B/2b)B/4c)Bd)2BCorrect answer is option 'D'. Can you explain this answer?
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