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A 50-turn coil has a diameter of 15 cm. The coil is placed in a spatially uniform magnetic field of magnitude 0.500~\text{T}0.500 T so that the plane of the coil makes an angle of 30^\circ30 ​∘ ​​ with the magnetic field. Find the magnitude of the emf induced in the coil if the magnetic field is reduced to zero uniformly in 0.100~\text{s}0.100 s.

Respuesta :

Answer:

3.9 V

Explanation:

Parameters given:

Number of turns, N = 50

Diameter of coil = 15 cm = 0.15 m

Radius of coil, r = 0.075 m

Magnetic field, B = 0.5 T

Angle = 30°

Time, t = 0.1 secs

E. M. F induced is given as:

EMF = (B * A * N * cos30) / t

Where A = area of coil = pi * r²

A = 3.142 * 0.075² = 0.018 m²

EMF = (0.5 * 0.018 * 50 * 0.866) / 0.1

EMF = 3.9 V

Cricetus

The magnitude to the EMF will be "3.8 V".

Given values:

  • N = 50
  • d = 15 cm, or 0.15 m
  • [tex]B_1[/tex] = 0.5 T
  • [tex]\Theta_1[/tex] = 30°
  • [tex]t_1[/tex] = 0.100 s

As we know the formula,

→ [tex]A = \frac{\pi d^2}{4}[/tex]

      [tex]= \frac{3.14\times (0.15)^2}{4}[/tex]

      [tex]= 0.0176625 \ m^2[/tex]

hence,

The EMF will be:

= [tex]\frac{A\times N\times B_1\times Cos \Theta_1}{t_1}[/tex]

By substituting the given values, we get

= [tex]\frac{0.0176625\times 50\times 0.5\times Cos 30^{\circ}}{0.100}[/tex]

= [tex]\frac{0.0176625\times 50\times 0.5\times 0.866}{0.100}[/tex]

= [tex]3.8 \ V[/tex]

Thus the above answer is right.

Learn more about magnetic field here:

https://brainly.com/question/13077711

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