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At what radial distance r from the center of a toroid of 150 windings does the magnitude of the magnetic field equal that found inside a solenoid that has 550 turns per meter of length? Assume that the current is the same through both devices.

Express your answer with the appropriate units.
Express your answer with the appropriate units.

Respuesta :

Answer:

The required radial distance from the center of the toroid is -

r = 4.34 cm

Explanation:

We know that magnetic field inside a solenoid is given by -

B = μni

where 'μ' is the magnetic permeability , 'n' is the number of turns per unit length , 'i' is the current passing through solenoid.

given n = 550  turns/meter

We know that magnetic field inside a toroid is -

B = μ×[tex]\frac{N}{2\pi r }[/tex]×i [Current is same in both the devices] , where 'N' is the total number of turns in the toroid and 'r' is the radial distance from the center of the toroid.

Given N = 150.

Equating the two magnetic fields , we get -

μni = μ×[tex]\frac{N}{2\pi r }[/tex]×i

∴ [tex]r = \frac{N}{2n\pi }[/tex]

Substituting the values we get -

r = 0.0434 m = 4.34 cm

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