JEE Main · 2025 · 23 Jan 2025 · Shift 2 · Chapter_pending

Match List-I with List-II.

Choose the correct answer from the options given below :

Answer: A → III, B → II, C → IV, D → I

Solution

Each quantity is pinned down from a defining physical relation.

Permeability of free space: from

B = \frac{μ _{0} I}{2 π r}

[μ_{0}] = \frac{[ B ] [ r ]}{[ I ]}

The magnetic field magnitude follows from the force law

F = q v B

[B] = \frac{[ F ]}{[ q ] [ v ]} = \frac{[ M L T ^{- 2} ]}{[ A T ] [ L T ^{- 1} ]} = [M T^{- 2} A^{- 1}]

[μ_{0}] = \frac{[ M T ^{- 2} A ^{- 1} ] [ L ]}{[ A ]} = [M L T^{- 2} A^{- 2}]

which matches (III).

Magnetic field: as found above,

[B] = [M T^{- 2} A^{- 1}]

, which matches (II).

Magnetic moment: since

M = N I A

(current times area),

[M] = [A] [L^{2}] = [L^{2} A]

which matches (IV).

Torsional constant: from

τ = c θ

(with

θ

dimensionless),

[c] = [τ] = [M L^{2} T^{- 2}]

which matches (I).

The matching is (A)-(III), (B)-(II), (C)-(IV), (D)-(I).

JEE Main · 2025 · 23 Jan 2025 · Shift 2 · Match the columns