Problem 61 - Master Resource Book in JEE Main Physics

Question

\(1 \mathrm{Wbm}^{-2}\) is equal to [UP SEE 2005] (a) \(10^{4}\) Gauss (b) \(4 \times 10^{-3}\) Gauss (c) \(10^{2}\) Gauss (d) \(10^{-4}\) Gauss

Step-by-Step Solution

Answer

1 Wbm\(^{-2}\) is equal to 10,000 Gauss (option a).

Step 1: Understand the Units

The unit Wbm² refers to Weber per meter squared, which is equivalent to Tesla (T) in the International System of Units (SI). This describes a magnetic flux density.

Step 2: Relation Between Tesla and Gauss

1 Tesla (T) is equivalent to 10,000 Gauss (G). This is a key conversion factor between SI units and Gaussian units used in magnetic fields.

Step 3: Convert Weber per Meter Squared to Gauss

Given that 1 Wbm² is equivalent to 1 Tesla, we can use the conversion factor between Tesla and Gauss to find the equivalent in Gauss: \[1 \text{ Tesla} = 10,000 \text{ Gauss} = 10^4 \text{ Gauss}.\] Hence, \[1 \text{ Wbm}^{-2} = 10^4 \text{ Gauss}.\]

Step 4: Match to the Given Options

Among the given options: (a) \(10^4 \text{ Gauss}\), (b) \(4 \times 10^{-3} \text{ Gauss}\), (c) \(10^2 \text{ Gauss}\), and (d) \(10^{-4} \text{ Gauss}\), the correct match is option (a) \(10^4 \text{ Gauss}\).

Key Concepts

Units of Measurement in Physics

In the realm of physics, units of measurement play a fundamental role in expressing quantities and defining the scale of operations across various physical phenomena.

• For magnetic flux density, the key unit in the International System of Units (SI) is the Tesla (T), named after the inventor Nikola Tesla.
• In the Gaussian or the cgs (centimeter-gram-second) system, the corresponding unit is the Gauss (G).
• This unit denotes the amount of magnetic flux passing through a unit area.

In standardized practice, using and converting these units correctly is essential to ensure the accuracy and precision of scientific computations and measurements. For example, one area might measure magnetic fields in Tesla, while another uses Gauss, so understanding these units allows scientists and engineers to communicate their findings universally.

Conversion between Tesla and Gauss

Conversion between Tesla and Gauss can often seem daunting, but with the established conversion factor it becomes straightforward.

• It's important to note that 1 Tesla is equivalent to 10,000 Gauss.
• This means that to convert a measurement from Tesla to Gauss, one simply multiplies the given Tesla value by 10,000.
• For example, 1 Tesla would equal 10,000 Gauss, which can also be expressed as \(10^4\) Gauss.

Conversely, converting Gauss back to Tesla involves dividing the Gauss measurement by 10,000. This simple conversion allows for coherent communication between systems that rely on different units and thus facilitates a unified understanding of magnetic flux density.

Magnetic Field Units in SI and Gaussian Systems

Understanding magnetic field units across different systems, specifically the SI and Gaussian systems, is crucial for physicists and engineers alike.

• The SI system predominantly uses Tesla (T) as its measurement for magnetic flux density.
• This unit provides a straightforward measure of the magnetic force per meter of current-carrying conductor.
• In contrast, the Gaussian system employs the Gauss (G), which is a smaller unit of measurement.

The distinction and ability to convert between these units ensure that scientific experiments and engineering projects remain consistent, irrespective of the system being used. This versatility also emphasizes the importance of selecting the correct measurement system for a given scientific inquiry or technological application.