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Two coils have the same number of circular turns and carry the same current. Each rotates in a magnetic field acting perpendicularly to its axis of rotation. Coil 1 has a radius of 5.6 cm and rotates in a 0.24-T field. Coil 2 rotates in a 0.44-T field. Each coil experiences the same maximum torque. What is the radius (in cm) of coil 2?

Respuesta :

Answer:

4.14 cm.

Explanation:

Given,

For Coil 1

radius of coil, r₁ = 5.6 cm

Magnetic field, B₁ = 0.24 T

For Coil 2

radius of coil, r₂ = ?

Magnetic field, B₂ = 0.44 T

Using formula of maximum torque

[tex]\tau_{max}= NIAB[/tex]

Since both the coil experience same maximum torques

now,

[tex] NIA_1B_1 = NIA_2B_2[/tex]

[tex]A_1B_1 = A_2B_2[/tex]

[tex] r_1^2 B_1 = r_2^2 B_2[/tex]

[tex] 5.6^2\times 0.24= r_2^2\times 0.44[/tex]

[tex]r_2 = 4.14\ cm[/tex]

Radius of the coil 2 is equal to 4.14 cm.

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