Chapter 7: Q10P (page 311)

A square loop (side a) is mounted on a vertical shaft and rotated at angular velocity $ω$ (Fig. 7.19). A uniform magnetic field B points to the right. Find the $ε (t)$ for this alternating current generator.

Short Answer

Expert verified

The induced emf in the square loop is . $B a^{2} ω \sin ω t$

Step by step solution

Write the given data from the question.

The uniform magnetic field is B .

The side of the square loop is a .

The angular velocity is $ω$ .

Calculate the generated emf in the square loop.

$ε (t) = - \frac{d}{d t} (B A \cos ω t)$ The area of square loop, $A = a^{2}$ .

The square loop is moving at angle with angular velocity in time

$t θ ω t$ .

The magnetic flus through the loop is given by,

role="math" localid="1657618600560"

ϕ = B A \cos θ

Substitute $ω t$ for $θ$ into above equation.

$ϕ = B A \cos θ$

According to the Faraday’s law, the induced emf in any closed loop is equal to the negative of the rate of change of flux in the circuit.

$ε (t) = - \frac{d ϕ}{d t}$

Substitute $ϕ = B A \cos ω t$ for $ϕ$ into above equation.

$ε (t) = - \frac{d}{d t} (B A \cos ω t)$

Substitute for into above equation.

role="math" localid="1657619049126" $ε (t) = - \frac{d}{d t} (B A \cos ω t) ε (t) = - B a^{2} (- \sin ω t) . ω ε (t) = - B a^{2} \sin ω t$

Hence the induced emf in the square loop is $B a^{2} ω \sin ω t$ .

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A square loop (side a) is mounted on a vertical shaft and rotated at angular velocity $ω$ (Fig. 7.19). A uniform magnetic field B points to the right. Find the $ε (t)$ for this alternating current generator.

Short Answer

Step by step solution

Write the given data from the question.

Calculate the generated emf in the square loop.

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A square loop (side a) is mounted on a vertical shaft and rotated at angular velocity ω (Fig. 7.19). A uniform magnetic field B points to the right. Find theεtfor this alternating current generator.

Short Answer

Step by step solution

Write the given data from the question.

Calculate the generated emf in the square loop.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Famous Physicists

Classical Mechanics

Electromagnetism

Astrophysics

Kinematics Physics

Oscillations

Study anywhere. Anytime. Across all devices.

A square loop (side a) is mounted on a vertical shaft and rotated at angular velocity $ω$ (Fig. 7.19). A uniform magnetic field B points to the right. Find the $ε (t)$ for this alternating current generator.