If E and H represent the intensity of electric field and magnetising field respectively, then the un

Q: Why is $H$ measured in $\text{A m}^{-1}$?

Magnetising field $H$ is related to the current creating the magnetic field. For a long solenoid, $H = nI$, where $n$ is turns per unit length ($\text{m}^{-1}$) and $I$ is current ($\text{A}$). Multiplying them gives $\text{A m}^{-1}$.

Q: Can we use dimensional formulas instead of units to solve this?

Absolutely! You can find the dimensional formula for $E$ and $H$ and divide them. You will get the dimensional formula for resistance $[\text{M L}^2 \text{T}^{-3} \text{A}^{-2}]$, which corresponds to ohms.

Q: What is the physical meaning of $E/H$?

It represents the wave impedance of a medium through which an electromagnetic wave is traveling. It tells us how much the medium resists the flow of the wave, much like resistance in a circuit.

Q: Is $H$ the same as magnetic field $B$?

No, $B$ is the magnetic flux density (measured in Tesla), while $H$ is the magnetising field intensity. They are related by the permeability of the medium: $B = \mu H$.

Q: What is the value of this ratio in a vacuum?

In a vacuum, the ratio $E/H$ is called the impedance of free space, denoted by $Z_0$, and its value is exactly $120\pi \, \Omega$, or approximately $377 \, \Omega$.

Question

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

Options:

(A) ohm

(B) mho

(C) joule

(D) newton

Sigma Percentile · Accepted Answer

### Analyzing the Setup

Let's embark on a journey to decode a very famous ratio in electromagnetic theory: the ratio of the electric field intensity, $E$, to the magnetising field intensity, $H$.

At first glance, it might seem like a simple exercise in units, but it holds a profound physical meaning. Our objective is to find the unit of the ratio $\frac{E}{H}$. To do this, we must first recall the individual units of these two fundamental fields.

### The Master Equation

The unit of electric field intensity, $E$, is defined as the potential difference per unit length. Therefore, its standard SI unit is volts per meter, or $	ext{V m}^{-1}$.

On the other hand, the magnetising field intensity, $H$, is related to the current that generates the magnetic field. For instance, in a long solenoid, $H = nI$, where $n$ is the number of turns per unit length and $I$ is the current. Thus, its unit is amperes per meter, or $	ext{A m}^{-1}$.

Now, let's set up our raw equation by substituting these units into our ratio:

$$	ext{Unit of } \frac{E}{H} = \frac{	ext{V m}^{-1}}{	ext{A m}^{-1}}$$

### Final Calculation

Look closely at the expression we just formed. The $	ext{m}^{-1}$ terms in both the numerator and the denominator cancel each other out perfectly.

This elegant cancellation leaves us with a much simpler fraction:

$$\frac{	ext{V m}^{-1}}{	ext{A m}^{-1}} = \frac{	ext{V}}{	ext{A}}$$

Does volts per ampere sound familiar? It absolutely should! According to Ohm's Law, resistance is the ratio of voltage to current ($R = \frac{V}{I}$). Therefore, volts per ampere is simply the definition of the **ohm** ($\Omega$).

**The unit of $\frac{E}{H}$ is ohm.**

### The Physical Significance

Why does the ratio of two fields give us a unit of resistance? In the realm of electromagnetic waves, the ratio $\frac{E}{H}$ is known as the **wave impedance** of a medium. It represents how much the medium "resists" the propagation of the electromagnetic wave.

For a vacuum (free space), this intrinsic impedance is denoted by $Z_0$ and has a constant value of approximately $377 \, \Omega$. It's a beautiful example of how dimensional analysis connects abstract fields to tangible circuit concepts!

Animated Solution for Physics - Physics and Measurement: If $E$ and $H$ represent the intensity of electric field and magnetising field respectively, then the unit of $E / H$ will be

Select Answer:

Visualized Solution

Understanding the Ratio

Units of $E$ and $H$

Substituting the Units

Simplifying the Expression

Ohm's Law Connection

Wave Impedance

The Sigma Insight: Dimensional Analysis

Analyzing the Setup

The Master Equation

Final Calculation

The Physical Significance

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Animated Solution for Physics - Physics and Measurement: .math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If E and H represent the intensity of electric field and magnetising field respectively, then the unit of E/H will be