Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Problem 143

The dimensional formula of magnetic flux is ............ (a) \(\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-2} \mathrm{~A}^{-1}\) (b) \(\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{1} \mathrm{~A}^{2}\) (c) \(\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-2} \mathrm{~A}^{2}\) (d) \(\mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^{1} \mathrm{~A}^{2}\)

Short Answer

Expert verified
The dimensional formula of magnetic flux is \(\mathrm{M^{1} L^{2} T^{-2} A^{-1}}\).

Step by step solution

01

Determine the dimensions of magnetic field (B)

We know that the magnetic field B has units of Tesla. Tesla is defined as Weber(Φ) / square meter, which means B has the dimensions of magnetic flux per area. To make it easier, let's write the dimensions of magnetic field (B) as \(\mathrm{[B]}\).
02

Determine the dimensions of area (A)

The dimensions of area (A) is given as square meter, which is represented as \(\mathrm{[A] = L^2}\), where L represents length.
03

Determine the dimensions of cos(θ)

Since the cosine function is a dimensionless quantity, the dimensions of cos(θ) are \(\mathrm{[cos(\theta)] = 1}\).
04

Get the dimensional formula of magnetic flux (Φ)

Now that we have the dimensions of B, A, and cos(θ), we can find the dimensions of magnetic flux (Φ): \[\mathrm{[\Phi] = [B] \times [A] \times [cos(\theta)]}\] As the dimension of cos(θ) is 1, it will not affect the dimensions. So, we can ignore it and write \(\mathrm{[\Phi] = [B] \times [A]}\).
05

Substitute the known dimensions

From step 1, we know the dimensions of B: \[\mathrm{[B] = \frac{[\Phi]}{[A]}}\] Now, substitute the dimensions of magnetic flux per area \((\mathrm{M^{1} L^{2} T^{-2} A^{-1}})\) for B and the dimensions of area \((\mathrm{L^2})\) for A: \[\mathrm{[\Phi] = (\frac{M^{1} L^{2} T^{-2} A^{-1}}{L^{2}}) \times L^{2}}\]
06

Solve for the dimensions of magnetic flux (Φ)

When we cancel out the L^2 in the numerator and denominator, we will get the following dimensional formula for magnetic flux: \[\mathrm{[\Phi] = M^{1} L^{2} T^{-2} A^{-1}}\] Therefore, the correct answer is option (a) \(\mathrm{M^{1} L^{2} T^{-2} A^{-1}}\).

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

The periodic time of simple pendulum is $\mathrm{T}=2 \pi \sqrt{(\ell / \mathrm{g})}\( relative error in the measurement of \)\mathrm{T}\( and \)\ell$ are \(\pm \mathrm{a}\) and \(\pm \mathrm{b}\) respectively find relative error in the measurement of \(g\) (a) \(a+b\) (b) \(2 \mathrm{~b}+\mathrm{a}\) (c) \(2 \mathrm{a}+\mathrm{b}\) (d) \(a-b\)

\(F=A_{0}\left(1-e^{-(B x t) 2}\right)\) where \(F\) is force and \(x\) is displacement. write the dimension formula of \(B\) (a) \(\mathrm{M}^{2} \mathrm{~L}^{1} \mathrm{~T}^{-1}\) (b) \(\mathrm{M}^{0} \mathrm{~L}^{-1} \mathrm{~T}^{-2}\) (c) \(\mathrm{M}^{1} \mathrm{~L}^{0} \mathrm{~T}^{-2}\) (d) \(\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-1}\)

Dimensional formula for Resistance (R) is ............. (a) \(\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-3} \mathrm{~A}^{-1}\) (b) \(\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{0} \mathrm{~A}^{-1}\) (c) \(\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-3} \mathrm{~A}^{-2}\) (d) \(\mathrm{M}^{1} \mathrm{~L}^{0} \mathrm{~T}^{-3} \mathrm{~A}^{-1}\)

What is the least count of vernier callipers? (a) \(10^{-4} \mathrm{~m}\) (b) \(10^{-5} \mathrm{~m}\) (c) \(10^{-2} \mathrm{~m}\) (d) \(10^{-3} \mathrm{~m}\)

Which of the following unit does not represent the unit of power? (a) ampere/volt (b) (ampere) \(^{2} \times \mathrm{ohm}\) (c) joule/second (d) ampere \(\times\) volt
See all solutions

Recommended explanations on English Textbooks

Lexis and Semantics Summary

Read Explanation

International English

Read Explanation

Lexis and Semantics

Read Explanation

Pragmatics

Read Explanation

Language and Social Groups

Read Explanation

Synthesis Essay

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