Question

Unit of \(\mu_{0} \mathrm{C}\) is same as that of (A) current (B) resistance (C) electric charge (D) velocity

Short answer

The unit of the given expression \(\mu_{0} \mathrm{C}\) is tesla meter (Tm). However, none of the options provided in the question match the unit of the given expression. Therefore, the correct answer is not provided in this list.

Step-by-step solution

Identify the units of the given quantities

The given expression is \(\mu_{0} \mathrm{C}\). We need to find the units of this expression. The units for each constant and quantity are as follows: 1. \(\mu_{0}\) (magnetic permeability constant): \( Tm/A \) (tesla meter per ampere) 2. \(\mathrm{C}\) (coulombs): \(A \cdot s \) (ampere seconds)

Multiply the units to find the unit of the expression

Now that we've identified the units of each quantity, we will multiply the units of \(\mu_{0}\) and \(\mathrm{C}\) to find the unit of the given expression: Unit of \(\mu_{0} \mathrm{C}\) = (Unit of \(\mu_{0}\)) × (Unit of \(\mathrm{C}\)) Unit of \(\mu_{0} \mathrm{C}\) = \( (Tm/A) \times (As) \) Unit of \(\mu_{0} \mathrm{C}\) = \( Tm \)

Compare with the given options

The unit of the given expression, \(Tm\), is tesla meter. Now we'll compare this unit with the units of the options provided in the question: (A) Current: The unit of current is ampere (A), which doesn't match with tesla meter (Tm). (B) Resistance: The unit of resistance is ohm (Ω), which also doesn't match with tesla meter (Tm). (C) Electric charge: The unit of electric charge is coulomb (C), which is not equal to tesla meter (Tm). (D) Velocity: The unit of velocity is meter per second (m/s), which doesn't match with tesla meter (Tm). Since none of the given options have a unit that matches the unit of the given expression, we can conclude that the correct answer is not provided in this list.

Key concepts

Magnetic permeability

Magnetic permeability, symbolized by \( \mu \), is a fundamental property in physics that describes how a material or a medium responds to a magnetic field. It measures the ability of a material to support the formation of a magnetic field within it. You can think of it as how easily the material allows magnetic field lines to pass through it.

• In a vacuum, the magnetic permeability is denoted as \( \mu_{0} \), often referred to as the permeability of free space.
• The standard unit for measuring permeability in the International System of Units (SI) is tesla meter per ampere, or \( Tm/A \).
• High permeability indicates materials that can easily become magnetized, like iron.

Understanding magnetic permeability is crucial for designing electromagnetic devices like transformers, inductors, and magnetic coils.The concept of permeability is applicable in solving various physics problems where magnetic fields interact with different materials.

Electric charge

Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electric field. It is quantized, meaning it exists in discrete amounts, and can be positive or negative.

• Protons carry a positive charge, while electrons carry a negative charge.
• The unit of electric charge in the SI system is the coulomb (\( C \)). A single electron carries a charge of approximately \(-1.6 \times 10^{-19}\) coulombs.
• Interactions between electric charges follow the principles of Coulomb's law, which describes the force between two charges as directly proportional to the product of the charges themselves, and inversely proportional to the square of the distance between them.

Electric charge is a pivotal concept in physics as it forms the basis of understanding electric fields, circuits, and electrostatics. It plays a key role in many physics problems, including those found in exams like the JEE Physics.

Tesla meter

The tesla meter, usually appearing in the context of magnetic flux density measurements, is an important term in electromagnetism. It is a compound unit stemming from the product of tesla and meter, signifying the magnetic field strength or magnetic flux density across a certain length.

• Tesla (T): The tesla is the SI derived unit of magnetic flux density. It is defined as one weber per square meter.
• Meter (m): Basic unit of length in the SI system used to measure distance.
• The combination of tesla and meter doesn't correspond to any of the conventional physical quantities like electric charge or current, which is why units like tesla meter sometimes confuse students when they appear in exam problems.

When solving physics problems, particularly those in an academic context like JEE Physics, understanding unit combinations such as tesla meter is essential to interpreting what the expressions and constants are describing.

Physics problems

Physics problems often challenge students to apply theoretical concepts to practical scenarios. They can range from simple calculations to complex logical deductions. Here's an approach to tackle them effectively:

• Understand the Question: Break down the problem statement to understand exactly what is being asked.
• Identify Knowns and Unknowns: List all the given quantities, constants, and what needs to be found.
• Choose the Right Formula: Based on the identified quantities, select the appropriate physics equations to use.
• Perform Unit Consistency Checks: Ensure all units are consistent when performing calculations to avoid errors.
• Logical Reasoning: Use reasoning to interpret the results and check if they make sense.

Many students use these steps in problem-solving but are often tripped up by unfamiliar units or constants. As seen in exams like the JEE Physics, successful tackling of such problems often requires a familiarity with both theoretical concepts and practical unit conversions.

JEE Physics

JEE Physics involves a deep comprehension of numerous physical laws and principles, striving to test students' understanding and problem-solving skills. Here’s what students should focus on:

• Conceptual Clarity: A strong grasp of fundamental concepts is vital since most questions are based on these basics.
• Application of Concepts: Learning to apply theoretical knowledge to solve complex problems is crucial.
• Familiarity with Formulas: Being aware of and quickly recalling formulas for different physics topics is essential.
• Practice with Previous Papers: Regular practice of past questions can help understand question patterns and frequently tested concepts.
• Time Management: Developing efficient time management strategies during the exam can significantly impact performance.

JEE Physics is known for its demanding nature, but with dedicated study and a strategic approach, mastering it is certainly achievable. This field forms a large part of the preparation for engineering entrance exams, emphasizing the importance of both calculations and conceptual understanding in solving physics problems.