Problem 29 - Master Resource Book in JEE Main Physics

Question

Which of the following is a unit of permeability (a) \(\mathrm{H} / \mathrm{m}\) (b) \(\mathrm{Wb} / \mathrm{Am}\) (c) ohm \(\times \mathrm{s} / \mathrm{m}\) (d) \(\mathrm{V} \times \mathrm{s} / \mathrm{m}^{2}\)

Step-by-Step Solution

Answer

The unit of permeability is H/m, which is option (a).

Step 1: Identify the Unit of Permeability

Permeability is a measure of how easily a material can support the formation of a magnetic field within itself. The standard unit of permeability in the International System of Units (SI) is the henry per meter (H/m).

Step 2: Analyze Given Options

Review the units provided in options (a) through (d): 1. Option (a) is H/m. 2. Option (b) is Wb/Am. 3. Option (c) is ohm × s/m. 4. Option (d) is V × s/m².

Step 3: Match the Correct Unit

Compare each option to the known unit of permeability, H/m. - Option (a) matches exactly as H/m. - Options (b), (c), and (d) do not match the unit for permeability as they represent different physical quantities or combinations.

Key Concepts

SI Units

The International System of Units, commonly abbreviated as SI, is the modern form of the metric system. It is used worldwide in science and industry to provide consistency and clarity. SI Units help in defining specific and standard measures for every physical quantity.For understanding the concept of magnetic permeability, it's important to know that SI Units play a crucial role. Magnetic permeability, which indicates how well a material can support a magnetic field, is expressed in henry per meter (\(\mathrm{H/m}\)) in SI Units.

• The basic purpose of SI Units is to provide a universally recognized framework for measurements.
• By using the same units globally, scientists and engineers can share and compare results with ease.
• Standardization of units prevents confusion that could result from differing measurement systems.

SI Units ensure that no matter where you are in the world, a measurement can be accurately understood and replicated.

Magnetic Fields

Magnetic fields are fascinating invisible forces that have many applications and impacts in the real world. These fields are produced by moving electric charges and certain materials known as magnets. A key point to understand about magnetic fields is their strength and interaction with materials. This is where the concept of magnetic permeability comes in. Magnetic permeability is the property of a material that helps it to conduct magnetism. It measures the degree to which a material can become magnetized in an external magnetic field.

• Highly permeable materials, like iron, enhance the magnetic field dramatically when placed in it.
• This concept is crucial in designing magnetic circuits and electronic devices.
• Understanding magnetic fields and permeability helps in the development of transformers, inductors, and motors.

This understanding of magnetic fields is applied in various technologies, leading to advancements in electronics and communication.

Physical Quantities

Physical quantities are measurable aspects of objects and phenomena in the physical world that can be expressed using numbers and units. They encompass everything from length, mass, and time to more complex concepts like force, energy, and magnetic permeability. When it comes to measuring magnetic permeability, we see how physical quantities quantify the ease with which a material allows a magnetic field to pass through it.

• Physical quantities allow us to apply mathematics to the real world, predicting how systems behave under certain conditions.
• They provide a bridge between theoretical concepts and practical applications.
• Accurate measurement of physical quantities is at the heart of experimental science and engineering.

By studying physical quantities, scientists can derive meaningful insights and develop new technologies. In this context, understanding magnetic permeability as a physical quantity aids in material science and various engineering fields.