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A flat coil having 160 turns, each with an area of 0.20 m 2, is placed with the plane of its area perpendicular to a magnetic field of 0.40 T. The magnetic field changes uniformly from 0.40 T in the + x direction to 0.40 T in the - x direction in 2.0 s. If the resistance of the coil is 16 Ω, at what rate is power generated in the coil during this change?

Respuesta :

Answer:

10.2 Watt

Explanation:

[tex]N[/tex]  = number of turns in flat coil = 160

[tex]A[/tex]  = area = 0.20 m²

B₀= initial magnetic field = 0.40 T

[tex]B[/tex]  = final magnetic field = - 0.40 T

Change in magnetic field is given as

ΔB = B - B₀ = - 0.40 - 0.40 = - 0.80 T

[tex]t[/tex]  = time taken for the magnetic field to change = 2.0 s

Induced emf is given as

[tex]E = \frac{- N A \Delta B}{t}[/tex]

[tex]E = \frac{- (160) (0.20) (- 0.80)}{2}[/tex]

[tex]E[/tex] = 12.8 volts

[tex]R[/tex] = Resistance of the coil = 16 Ω

Power is given as

[tex]P = \frac{E^{2}}{R}[/tex]

[tex]P = \frac{(12.8)^{2}}{16}[/tex]

[tex]P[/tex] = 10.2 Watt

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