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Physics · Units, Dimensions & Error Analysis

JEE Advanced 2018 — Paper 1 — Question 41

In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, [E][E] and [B][B] stand for dimensions of electric and magnetic fields respectively, while [ϵ0]\left[\epsilon_{0}\right] and [μ0]\left[\mu_{0}\right] stand for dimensions of the permittivity and permeability of free space respectively. [L] and [T][T] are dimensions of length and time respectively. All the quantities are given in SI units.

The relation between [E][E] and [B][B] is

  1. Option A:

    [E]=[B][E] = [B] [L][L] [T][T]

  2. Option B:

    [E]=[B][E] = [B] [L]−1[L]^{-1} [T][T]

  3. Option C:

    [E]=[B][E] = [B] [L][L] [T]−1[T]^{-1}

    Correct
  4. Option D:

    [E]=[B][E] = [B] [L]−1[L]^{-1} [T]−1[T]^{-1}

Answer: C

Step-by-step solution

E=FqE = \frac{F}{q}; F=qvBF = qvB

E=BvE = Bv; [E]=[B][L][T]−1[E] = [B][L][T]^{-1}

Answer key and solution verified before publishing.

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Exam
JEE Advanced 2018
Paper
Paper 1
Subject
Physics
Chapter
Units, Dimensions & Error Analysis
Topic
Units and Dimensions Analysis

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