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Physics Question 27 – JEE-MAIN 2026

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Consider the equation H=xpϵqErts Where H=magnetic field; E=electric field, ϵ=permittivity, x=distance, t=time The values of p,q,r and s respectively are :

The problem requires finding the powers of physical quantities in an equation by ensuring dimensional consistency on both sides.

Step 1: Determine Dimensions of Each Quantity✦ Active

First, identify the dimensions of each physical quantity involved in the equation in terms of fundamental units (Mass M, Length L, Time T, Electric Current A):

H=[AL−1] E=[MLT−3A−1] ϵ=[M−1L−3T4A2] x=[L] t=[T]

The given equation is H=xpϵqErt−s.

Step 2: Equate Dimensions on Both Sides○ Expand

Substitute the dimensions into the equation and combine the powers of each fundamental dimension:

[AL−1]=[L]p[M−1L−3T4A2]q[MLT−3A−1]r[T]−s [M0L−1T0A1]=[M−q+r][Lp−3q+r][T4q−3r−s][A2q−r]
💡 Teacher's Secret Hint

Ensure all exponents are correctly distributed and combined for each fundamental dimension.

Step 3: Solve the System of Equations○ Expand

Equate the powers of M, L, T, and A on both sides to form a system of linear equations:

M:0=−q+r(1) L:−1=p−3q+r(2) T:0=4q−3r−s(3) A:1=2q−r(4)

From (1), q=r. Substitute this into (4): 1=2q−q⟹q=1. Therefore, r=1.

Substitute q=1 and r=1 into (2): −1=p−3(1)+1⟹−1=p−2⟹p=1.

Substitute q=1 and r=1 into (3): 0=4(1)−3(1)−s⟹0=1−s⟹s=1.

Thus, the values are p=1,q=1,r=1,s=1.

💡 Teacher's Secret Hint

Carefully solve the system of equations step-by-step to avoid algebraic errors.

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