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MCQEasyJEE 2025Dimensions & Dimensional Analysis

JEE Physics 2025 Question with Solution

In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of MQLRTSAP\mathrm{M}^{Q} \mathrm{L}^{R} \mathrm{T}^{S} \mathrm{A}^{P}, where value of 'Q' and 'R' are

  • A

    (3,−5)\left(3,-5\right)

  • B

    (−2,2)\left(-2,2\right)

  • C

    (−2,1)\left(-2,1\right)

  • D

    (1,−1)\left(1,-1\right)

Answer

Correct answer:D

Step-by-step solution

Standard Method

Given: We need the dimensions of the ratio of electric flux to magnetic flux.

Find: The values corresponding to the exponents asked in the dimensional form.

Electric flux and magnetic flux are

ϕE=EA\phi_E = EA

and

ϕM=BA\phi_M = BA

So,

ϕEϕM=EB\frac{\phi_E}{\phi_M} = \frac{E}{B}

Now use the dimensions of electric field and magnetic field:

[E]=MLT−3A−1[E] = MLT^{-3}A^{-1} [B]=MT−2A−1[B] = MT^{-2}A^{-1}

Hence,

[EB]=MLT−3A−1MT−2A−1=LT−1\left[\frac{E}{B}\right] = \frac{MLT^{-3}A^{-1}}{MT^{-2}A^{-1}} = LT^{-1}

Therefore the powers are exponent of L=1L = 1 and exponent of T=−1T = -1, with no dependence on MM and AA.

Therefore, the correct option is D, i.e. (1,−1)\left(1,-1\right).

Using flux definitions

The area factor cancels in the ratio because both electric flux and magnetic flux are proportional to area:

ϕE=EA,ϕM=BA\phi_E = EA, \qquad \phi_M = BA

Therefore,

ϕEϕM=EABA=EB\frac{\phi_E}{\phi_M} = \frac{EA}{BA} = \frac{E}{B}

Using

[E]=MLT−3A−1,[B]=MT−2A−1[E] = MLT^{-3}A^{-1}, \qquad [B] = MT^{-2}A^{-1}

we get

[EB]=LT−1\left[\frac{E}{B}\right] = LT^{-1}

So the required pair is (1,−1)\left(1,-1\right).

Common mistakes

  • Using the wrong dimensions of electric field. The solution incorrectly shows [E]=MLT−2A−1[E] = MLT^{-2}A^{-1} at one place, but the correct dimension is [E]=MLT−3A−1[E] = MLT^{-3}A^{-1}. Use the standard SI dimensional formula before taking the ratio.

  • Forgetting that both electric flux and magnetic flux contain the same area factor. Since ϕE=EA\phi_E = EA and ϕM=BA\phi_M = BA, the area cancels and the ratio reduces to E/BE/B.

  • Matching the option pair to the wrong exponents. After obtaining LT−1LT^{-1}, identify carefully which two exponents the question is asking for before selecting the option.

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