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JEE PYQ: Units & Measurements - Question ID 558703b9db5e (JEE Main 2021)

ID: 558703b9db5eJEE Main 2021Single Correct MCQ

If E and H represents the intensity of electric field and magnetising field respectively, then the unit of E/H will be :

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Step-by-step Explanation

Core Formula & Concept:

In electromagnetism, the intensity of the electric field ( $E$ ) and the magnetising field ( $H$ ) are related through Maxwell’s equations. A key result from these equations is that the ratio $E/H$ has the dimensions of impedance, specifically the intrinsic impedance of free space, denoted $\eta_0$ .

The fundamental relation is: $\eta_0 = \frac{E}{H} = \sqrt{\frac{\mu_0}{\epsilon_0}}$ where

$\mu_0$ is the permeability of free space (unit: henry per metre, H/m),
$\epsilon_0$ is the permittivity of free space (unit: farad per metre, F/m).

Since

\sqrt{\frac{\mu_0}{\epsilon_0}}

has the unit of ohm (Ω), the ratio

E/H

must also have the unit ohm.

Step-by-Step Derivation:

Step 1: Write down the units of $E$ and $H$ .

Electric field intensity $E$ is measured in volt per metre (V/m).
Magnetising field $H$ is measured in ampere per metre (A/m).

Step 2: Form the ratio $E/H$ and express it in base units.

\frac{E}{H} = \frac{\text{V/m}}{\text{A/m}} = \frac{\text{V}}{\text{A}}

Step 3: Recall the definition of ohm.

The unit ohm (Ω) is defined as volt per ampere:

1\;\Omega = 1\;\frac{\text{V}}{\text{A}}

Step 4: Conclude the unit of $E/H$ .

Since

\frac{E}{H} = \frac{\text{V}}{\text{A}}

, it follows that

\text{Unit of } \frac{E}{H} = \Omega = \text{ohm}.

Step 5: Match with the given options.

The only option that corresponds to ohm is A: ohm. Common Traps & Exam Tip:

Many students confuse the units of $E$ and $H$ with those of $D$ (electric displacement) or $B$ (magnetic flux density). Remember:

$E$ is in V/m, not C/m².
$H$ is in A/m, not T (tesla).

If you mistakenly use

B

instead of

H

, you would get

\frac{E}{B}

in m/s (speed), which is not among the options. Always double-check which field (

E

H

) is asked for in the ratio.

JEE PYQ: Units & Measurements - Question ID 558703b9db5e (JEE Main 2021)

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Step-by-step Explanation

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