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 long, horizontal wire AB rests on the surface of a table and carries a current I. Horizontal wire CD is vertically above wire AB and is free to slide up and down on the two vertical metal guides C and D (Fig. E28.32). Wire CD is connected through the sliding contacts to another wire that also carries a current I, opposite in direction to the current in wire AB. The mass per unit length of the wire CD is l. To what equilibrium height h will the wire CD rise, assuming that the magnetic force on it is due entirely to the current in the wire AB?

Short Answer

Expert verified

The magnitude of the height the wire CD reaches is μ0l22πgλ .

Step by step solution

01

Identification of the concept.

The rod will be experiencing a downward pull by gravity. So, the upward force will move the wire CD in an upward direction until it is completely balanced by the gravitational force, which will cause the system to go under equilibrium.

Refer to the image below.

Since the currents are in opposite directions, therefore, the force experienced will be repulsive in nature

02

 Determination of the height at the wire CD rises

Magnetic force per length due to a current-carrying wire is given as,

FL=μ02πr

Substituting values in the above expression, and we get,

Fl=μ0I2L2πh

Here, L is the length of the wires, and h is the distance between them.

The gravitational force expression is,

mg=λLg

Now, the mechanism of forces acting is,

F1mg=0μ0I2L2πh=λLgh=μ0I22πgλ

Thus, h depends on the current I and also λ. The more the current or less λ, the larger the height h is. The value of h is μ0l22πgλ .

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 5.00-A current runs through a 12-gauge copper wire (diameter

2.05 mm) and through a light bulb. Copper has8.5×108free electrons per

cubic meter. (a) How many electrons pass through the light bulb each

second? (b) What is the current density in the wire? (c) At what speed does

a typical electron pass by any given point in the wire? (d) If you were to use

wire of twice the diameter, which of the above answers would change?

Would they increase or decrease?

Electric eels generate electric pulses along their skin that can be used to stun an enemy when they come into contact with it. Tests have shown that these pulses can be up to 500V and produce currents of 80mA(or even larger). A typical pulse lasts for 10ms. What power and how much energy are delivered to the unfortunate enemy with a single pulse, assuming a steady current?

A 1500-W electric heater is plugged into the outlet of a 120-V circuit that has a 20-A circuit breaker. You plug an electric hair dryer into the same outlet. The hair dryer has power settings of 600 W, 900 W, 1200 W, and 1500 W. You start with the hair dryer on the 600-W setting and increase the power setting until the circuit breaker trips. What power setting caused the breaker to trip?

In the circuit shown in Fig. E26.41, both capacitors are initially charged to 45.0 V. (a) How long after closing the switch S will the potential across each capacitor be reduced to 10.0 V, and (b) what will be the current at that time?

BIO Transmission of Nerve Impulses. Nerve cells transmit electric

signals through their long tubular axons. These signals propagate due to a

sudden rush of Na+ions, each with charge +e, into the axon. Measurements

have revealed that typically about 5.6×1011Na+ions enter each meter of the

axon during a time of . What is the current during this inflow of charge

in a meter of axon?

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