/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 20 A metal hoop is laid flat on the... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 29: Problem 20

A metal hoop is laid flat on the ground. A magnetic field that is directed upward, out of the ground, is increasing in magnitude. As you look down on the hoop from above, what is the direction of the induced current in the hoop?

Short Answer

Expert verified
Answer: The induced current in the hoop is clockwise.

Step by step solution

01

Understand Faraday's Law

Faraday's Law of electromagnetic induction states that the electromotive force (EMF) induced in a closed loop is equal to the negative rate of change of magnetic flux through the loop. Mathematically, it is expressed as: \(\text{EMF} = - \frac{d \Phi_B}{dt}\) Where \(\Phi_B\) is the magnetic flux and \(t\) is time. The induced current in the hoop will create a magnetic field that opposes the change in the external magnetic field, as stated by Lenz's law.
02

Determine the direction of the change in magnetic flux

In this case, the magnetic field is increasing in magnitude and is directed upward, out of the ground. This means that the change in magnetic flux is also upward.
03

Apply the right-hand rule

To determine the direction of the induced current, we can use the right-hand rule. The right-hand rule states that if we point our thumb in the direction of the magnetic field and curl our fingers, the direction of our fingers represents the direction of the induced current. Since the change in magnetic flux is upward, point the thumb of your right hand upward. Curl your fingers around the hoop, and the direction in which your fingers curl is the direction of the induced current.
04

Determine the direction of the induced current

From Step 3, when pointing your right thumb upward, your fingers will curl around the hoop in a clockwise direction (when looking down at the hoop from above). Therefore, the induced current in the hoop is clockwise.

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 91影视!

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

Which of the following will induce a current in a loop of wire in a uniform magnetic field? a) decreasing the strength of the field b) rotating the loop about an axis parallel to the field c) moving the loop within the field d) all of the above e) none of the above

A short coil with radius \(R=10.0 \mathrm{~cm}\) contains \(N=30.0\) turns and surrounds a long solenoid with radius \(r=8.00 \mathrm{~cm}\) containing \(n=60\) turns per centimeter. The current in the short coil is increased at a constant rate from zero to \(i=2.00 \mathrm{~A}\) in a time of \(t=12.0 \mathrm{~s}\). Calculate the induced potential difference in the long solenoid while the current is increasing in the short coil.

A circular coil of wire with 20 turns and a radius of \(40.0 \mathrm{~cm}\) is laying flat on a horizontal table as shown in the figure. There is a uniform magnetic field extending over the entire table with a magnitude of \(5.00 \mathrm{~T}\) and directed to the north and downward, making an angle of \(25.8^{\circ}\) with the horizontal. What is the magnitude of the magnetic flux through the coil?

Having just learned that there is energy associated with magnetic fields, an inventor sets out to tap the energy associated with the Earth's magnetic field. What volume of space near Earth's surface contains \(1 \mathrm{~J}\) of energy, assuming the strength of the magnetic field to be \(5.0 \cdot 10^{-5} \mathrm{~T} ?\)

A steel cylinder with radius \(2.5 \mathrm{~cm}\) and length \(10.0 \mathrm{~cm}\) rolls without slipping down a ramp that is inclined at \(15^{\circ}\) above the horizontal and has a length (along the ramp) of \(3.0 \mathrm{~m} .\) What is the induced potential difference between the ends of the cylinder at the bottom of the ramp, if the surface of the ramp points along magnetic north?
See all solutions

Recommended explanations on Physics Textbooks

Torque and Rotational Motion

Read Explanation

Physics of Motion

Read Explanation

Waves Physics

Read Explanation

Turning Points in Physics

Read Explanation

Electricity

Read Explanation

Fields in Physics

Read Explanation
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.