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

A 2.50mHtoroidal solenoid has an average radius of 6.00cmand a cross-sectional area of 2.00V. (a) How many coils does it have? (Make the same assumption as in Example 30.3.) (b) At what rate must the current through it change so that a potential difference of 2.00Vis developed across its ends?

Short Answer

Expert verified

(a) the toroidal solenoid has1940coils.

(b) the current rate for potential difference to be2.00Vdeveloped across its ends is800A/s

Step by step solution

01

Define self-induction and self-inductance of toroidal solenoid

Induction of an electromotive force in a circuit by a varying current in the same circuit, is called self-induction.

Self-inductance is measure of self-induction in circuit. It is expressed as,

ε=-LdIdtwhere εis induced emf, dIdtis rate at which current changes and L is the self-inductance.

Self-inductance of toroidal solenoidal is,

L=μ0N2A2πrwhere Lis self-inductance of toroid having N turns, Aarea of cross-section and 2πrbe circumference.

02

Apply the formulae

(a) The self-inductance L=2.50mHtoroidal solenoid has an average radius of r=6.00cmand a cross-sectional area of A=2.00cm2.

The number of coils Nin the toroid is,

L=μ0N2A2πrN=2π×0.0600×2.50×10-34π×10-7×2.00×10-4N=1940

(b) The magnitude of potential difference across the coil is expressed as,

|ε|=LdIdt

dIdt=εL

dIdt=2.002.50×10-3dIdt=800A/s

From above, current rate required to have ε=2.00Vpotential difference is given as,

Therefore, (a) the toroidal solenoid has1940coils;(b) the current rate for potential difference to be2.00Vdeveloped across its ends is800A/s.

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

(a) At room temperature, what is the strength of the electric field in a

12-gauge copper wire (diameter 2.05mm) that is needed to cause a 4.50-A

current to flow? (b) What field would be needed if the wire were made of silver

instead?

CALC The region between two concentric conducting spheres with radii and is filled with a conducting material with resistivity ρ. (a) Show that the resistance between the spheres is given by

R=ρ4π(1a-1b)

(b) Derive an expression for the current density as a function of radius, in terms of the potential differenceVab between the spheres. (c) Show that the result in part (a) reduces to Eq. (25.10) when the separation L=b-abetween the spheres is small.

In the circuit of Fig. E25.30, the 5.0 Ω resistor is removed and replaced by a resistor of unknown resistance R. When this is done, an ideal voltmeter connected across the points band creads 1.9 V. Find (a) the current in the circuit and (b) the resistance R. (c) Graph the potential rises and drops in this circuit (see Fig. 25.20).

BIO The average bulk resistivity of the human body (apart from surface resistance of the skin) is about 5.0Ω·m. The conducting path between the hands can be represented approximately as a cylinder 1.6 m long and 0.10 m in diameter. The skin resistance can be made negligible bysoaking the hands in salt water. (a) What is the resistance between the hands if the skin resistance is negligible? (b) What potential difference between thehands is needed for a lethal shock current of 100 mA ? (Note that your result shows that small potential differences produce dangerous currents when the skin is damp.) (c) With the current in part (b),what power is dissipated in the body?

High-voltage power supplies are sometimes designed intentionally to have rather large internal resistance as a safety precaution. Why is such a power supply with a large internal resistance safer than a supply with the same voltage but lower internal resistance?

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