Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Question: An electric generator contains a coil of 100 turnsof wire, each forming a rectangular loop 50.0cm to 30.0cm. The coil is placed entirely in a uniform magnetic field with magnitude B = 3.50 Tand withBinitially perpendicular to the coil’s plane. What is the maximum value of the emf produced when the coil is spun at 1000 rev/min about an axis perpendicular toB?

Short Answer

Expert verified

The maximum value of emf is,ε=5.5kV.

Step by step solution

01

Step 1: Given

  1. Turns of wire N = 100
  2. Rectangular loop dimension 50.0 cm by 30.0 cm
  3. Magnetic field B = 3.50 T
  4. Coil rotation 1000 rev/min
02

Determining the concept

From Faraday’s law, evaluate the induced emf from the number of turns and the change in the magnetic field lines that pass through the loop. Find the magnetic field lines with the given magnetic field and the area of the rectangular loop.

Faraday's law of electromagnetic inductionstates, Whenever a conductor is placed in a varying magnetic field, an electromotive force is induced in it.

Formulae are as follows:

ϕ=B.dAε=-Ndϕdt

Where,ϕ is magnetic flux, B is magnetic field, A is area, 𝜀 is emf, Nis number of turns.

03

Determining the maximum value of emf

The coil rotation is,

1000rev/min=1000rev1min×1min60s×2πrad1rev=104.7rad/secω=104.7rad/sec

The magnetic field lines ϕwith the given magnetic field and the area of the rectangular loop is given as,

ϕ=B.dAϕ=BdAcosθ

Butθ=ωtrad

ϕ=BdAcosωtϕ=BdAcosωt

By differentiating the magnetic field lines with respect to time,

dϕdt=ddtBAcosωtdϕdt=-ωBAcosωt

From Faraday’s law, induced emf,

ε=-Ndϕdtε=-N-ωBAsinωt=NωBAsinε=100×104.7×3.5×0.5×0.3sinωt

The induced emf will be maximum, when sinωt=1.

ε=100×104.7rad/s×3.5T×0.5m×0.3m×1ε=5.496×1035.5kV

Hence, the maximum value of emf is, ε=5.5kV.

Therefore, the induced emf in an electric generator can be determined using Faraday’s law when a coil of wire is wounded with the given number of turns.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Figure (a), a uniform magnetic field increases in magnitude with time t as given by Figure (b), where the vertical axis scale is set by Bs=9.0mTand the horizontal scale is set by ts=3.0sA circular conducting loop of area 8.0×10-4m2lies in the field, in the plane of the page. The amount of charge q passing point A on the loop is given in Figure (c) as a function of t, with the vertical axis scale set by qs=3.0s and the horizontal axis scale again set by localid="1661854094654" ts=3.0s. What is the loop’s resistance?

A coil is connected in series with a 10.0kresistor. An ideal 50.0 Vbattery is applied across the two devices, and the current reaches a value of 2.00 mAafter 5.00 ms.(a) Find the inductance of the coil. (b) How much energy is stored in the coil at this same moment?

In Fig. 30-23, a long straight wire with current ipasses (without touching) three rectangular wire loops with edge lengths L, 1.5L, and 2L. The loops are widely spaced (so as not to affect one another). Loops 1 and 3 are symmetric about the long wire. Rank the loops according to the size of the current induced in them if current iis (a) constant and (b) increasing, greatest first.

In Fig. 30-77,R1=8.0Ω,R2=10Ω,L1=0.30H,L2=0.20Hand the ideal battery hasε=6.0V. (a) Just after switch S is closed, at what rate is the current in inductor 1 changing? (b) When the circuit is in the steady state, what is the current in inductor 1?

The inductance of a closely packed coil of 400 turnsis 8.0 mH. Calculate the magnetic flux through the coil when the current is 5.0 mA.

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free