Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 13: Problem 1892

Two similar coils are kept mutually perpendicular such that their centers co- inside. At the centre, find the ratio of the mag. field due to one coil and the resultant magnetic field by both coils, if the same current is flown. (a) \(1: \sqrt{2}\) (b) \(1: 2\) (c) \(2: 1\) (d) \(\sqrt{3}: 1\)

Short Answer

Expert verified
The ratio of the magnetic field due to one coil and the resultant magnetic field by both coils is 1:√2. The correct answer is (a) 1:\(\sqrt{2}\).

Step by step solution

01

Determine the Magnetic Field due to One Coil

First, we need to find the magnetic field due to one coil at the center. Since the coils are similar and the current is the same in both coils, the magnetic field due to one coil will be equal to the magnetic field of the other coil. Let's call this magnetic field B1. For a circular coil with current I and N turns, the magnetic field B at the center can be calculated using the formula: \[B = \frac{\mu_0}{4 \pi}\frac{2 \pi NI}{R}\] Since we're dealing with only one coil here, N = 1. Now, the equation becomes: \[B1 = \frac{\mu_0 I}{2R}\]
02

Determine the Magnetic Field due to Both Coils

Now, we will find the magnetic field due to both coils at the center. Since the coils are mutually perpendicular, their magnetic fields will be orthogonal to each other, and the resultant magnetic field can be calculated using the Pythagorean theorem. Thus, the magnetic field due to both coils, B_total, can be found as: \[B_{total} = \sqrt{B1^2 + B2^2}\] Since the coils are similar and have the same current, B1 = B2, so: \[B_{total} = \sqrt{B1^2 + B1^2} = B1\sqrt{2}\]
03

Calculate the Ratio of Magnetic Fields

We now have the magnetic field due to one coil (B1) and the total magnetic field due to both coils (B_total). To find the required ratio, we divide the total magnetic field by the magnetic field due to one coil: \[\frac{B1}{B_{total}} = \frac{B1}{B1\sqrt{2}} = \frac{1}{\sqrt{2}}\] So, the ratio of the magnetic field due to one coil and the resultant magnetic field by both coils is 1:√2. The correct answer is (a) 1:\(\sqrt{2}\).

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.

Start your free trial

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 current of a \(1 \mathrm{Amp}\) is passed through a straight wire of length 2 meter. The magnetic field at a point in air at a distance of 3 meters from either end of wire and lying on the axis of wire will be (a) \(\left(\mu_{0} / 2 \pi\right)\) (b) \(\left(\mu_{0} / 4 \pi\right)\) (c) \(\left(\mu_{0} / 8 \pi\right)\) (d) zero

The mag. field (B) at the centre of a circular coil of radius "a", through which a current I flows is (a) \(\mathrm{B} \propto \mathrm{c} \mathrm{a}\) (b) \(\mathrm{B} \propto(1 / \mathrm{I})\) (c) \(\mathrm{B} \propto \mathrm{I}\) (d) \(B \propto I^{2}\)

A magnet of length \(0.1 \mathrm{~m}\) and pole strength $10^{-4} \mathrm{~A} \mathrm{~m} .$ is kept in a magnetic field of 30 tesla at an angle of 300 . The Torque acting on it is \(\times 10^{-4}\) Joule. (a) \(7.5\) (b) 3 (c) \(1.5\) (d) 6

If a long hollow copper pipe carries a direct current, the magnetic field associated with the current will be (a) Only inside the pipe (b) Only outside the pipe (c) Neither inside nor outside the pipe (d) Both inside and outside the pipe

1: A charged particle moves in a uniform mag. field. The velocity of the particle at some instant makes an acute angle with the mag. field. The path of the particle will be (a) A straight line (b) A circle (c) A helix with uniform pitch (d) A helix with non-uniform pitch
See all solutions

Recommended explanations on English Textbooks

Sociolinguistics

Read Explanation

5 Paragraph Essay

Read Explanation

Essay Plan

Read Explanation

Semiotics

Read Explanation

Email

Read Explanation

Syntax

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.

Sign-up for free