Chapter 30: Q82P (page 901)

A uniform magnetic field is perpendicular to the plane of a circular wire loop of radius r. The magnitude of the field varies with time according to $B = B_{0} e^{(- \frac{t}{τ})}$ , where $B_{0}$ and $τ$ are constants. Find an expression for the emf in the loop as a function of time.

Short Answer

Expert verified

Equation for the emf in the loop as a function of time will be

$\frac{B_{0} π r^{2}}{τ} (e^{(- \frac{t}{τ})})$

Step by step solution

Given

$B = B_{0} e^{(- \frac{t}{τ})}$

Understanding the concept

We use Lenz’s law for induced emf, we rearrange the formula to get the equation for the emf in the loop as a function of time.

Formula:

$ε = - N \frac{d ϕ}{d t}$

$ϕ = B A$

Calculate the Equation for the emf in the loop as a function of time

We have,

$ε = - \frac{d ϕ}{d t}$

We also have,

$ϕ = B A$

Here,

As the cross-section is circular,

$A = π r^{2}$

$ϕ = B π r^{2}$

We also have,

$B = B_{0} e^{(- \frac{t}{τ})} ϕ = (B_{0} e^{(- \frac{t}{τ})}) π r^{2} ε = - \frac{d ((B_{0} e^{(- \frac{t}{τ})}) π r^{2})}{d t} ε = B_{0} π r^{2} e^{(- \frac{t}{τ})} (- \frac{t}{τ}) ε = \frac{B_{0} π r^{2} e}{τ} (e^{(- \frac{t}{τ})})$

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A uniform magnetic field is perpendicular to the plane of a circular wire loop of radius r. The magnitude of the field varies with time according to $B = B_{0} e^{(- \frac{t}{τ})}$ , where $B_{0}$ and $τ$ are constants. Find an expression for the emf in the loop as a function of time.

Short Answer

Step by step solution

Given

Understanding the concept

Calculate the Equation for the emf in the loop as a function of time

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A uniform magnetic field is perpendicular to the plane of a circular wire loop of radius r. The magnitude of the field varies with time according toB=B0e(-tτ), whereB0andτare constants. Find an expression for the emf in the loop as a function of time.

Short Answer

Step by step solution

Given

Understanding the concept

Calculate the Equation for the emf in the loop as a function of time

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Classical Mechanics

Waves Physics

Fluids

Further Mechanics and Thermal Physics

Geometrical and Physical Optics

Torque and Rotational Motion

Study anywhere. Anytime. Across all devices.

A uniform magnetic field is perpendicular to the plane of a circular wire loop of radius r. The magnitude of the field varies with time according to $B = B_{0} e^{(- \frac{t}{τ})}$ , where $B_{0}$ and $τ$ are constants. Find an expression for the emf in the loop as a function of time.