Problem 37 - University Physics with Modern Physics

Question

A horizontal rod 0.200 \(\mathrm{m}\) long is mounted on a balance and carries a current. At the location of the rod a uniform horizontal magnetic field has magnitude 0.067 T and direction perpendicular to the rod. The magnetic force on the rod is measured by the balance and is found to be 0.13 \(\mathrm{N}\) . What is the current?

Step-by-Step Solution

Answer

The current is approximately 9.70 A.

Step 1: Understand the Formula for Magnetic Force

The magnetic force acting on a current-carrying conductor in a magnetic field is given by the formula: \[ F = BIL \]where \( F \) is the magnetic force, \( B \) is the magnetic field strength, \( I \) is the current, and \( L \) is the length of the conductor.

Step 2: Rearrange the Formula for Current

We need to find the current \( I \). Rearrange the formula to solve for \( I \):\[ I = \frac{F}{BL} \]

Step 3: Substitute Known Values

Substitute the given values for the force \( F = 0.13 \, \text{N} \), magnetic field \( B = 0.067 \, \text{T} \), and length \( L = 0.200 \, \text{m} \) into the formula:\[ I = \frac{0.13}{0.067 \times 0.200} \]

Step 4: Calculate the Current

Perform the multiplication and division to find the current:\[ I = \frac{0.13}{0.0134} \approx 9.70 \, \text{A} \]

Key Concepts

Current in Conductors

Current in conductors is a crucial concept in understanding how electricity and magnetism interact in physical systems. When an electrical current flows through a conductor, such as a wire or rod, it creates its own magnetic field around it. This phenomenon is fundamental to electromagnetism and can be observed in various applications like electromagnets and electric motors.

In conductors, current is simply the flow of electric charge, typically carried by electrons. It is measured in amperes (A) and can be calculated using Ohm's Law if the resistance and voltage across the conductor are known. However, in the scenario of a current-carrying conductor within an existing magnetic field, additional forces are at play.

Understanding these interactions helps in figuring out the magnetic force exerted when conductors are placed in magnetic fields. This force is vital in devices that rely on precise control of magnetic forces, such as loudspeakers and measuring instruments. Always remember the direction of the current influences the direction of the magnetic field generated around the conductor.

Magnetic Field

A magnetic field represents a region around a magnet where magnetic forces can be experienced. It is depicted by field lines that emanate from the north pole to the south pole of a magnet. These field lines are invisible but can be visualized using iron filings on a sheet of paper over a magnet.

The magnetic field is measured in Tesla (T) and can vary in strength and direction. In the context of a conductor within a magnetic field, the field interacts with the current flowing through the conductor to produce a force. This interaction is described by the Lorentz force law and is an essential part of electromagnetic theory.

• Field strength ( B ) indicates how strong the magnetic effect is at any given point.
• The direction of the magnetic field is crucial, particularly in determining the direction of the force on a current-carrying rod.

Understanding magnetic fields is key to navigating physics problems involving electromechanical systems, where both magnetic and electrical components are involved.

Physics Problem Solving

Physics problem solving is a methodical process that involves understanding and applying physical principles to a particular scenario. The exercise, for instance, where you calculate the current in a conductor influenced by a magnetic field, is a classic physics problem.

The steps include:

• Identifying the relevant physical principles, such as the magnetic force formula in this example.
• Re-arranging equations to isolate the unknown variable. In this case, it involved solving for current ( I ).
• Substituting known values, which requires careful units handling, to ensure consistency and accuracy in calculations.
• Performing calculations accurately, often needing careful multiplication and division to find the solution.

By understanding this process, students improve their ability to break down complex problems into simpler, manageable parts. This strategy enhances comprehension and reinforces core physics concepts, making it easier to tackle a wide range of problems.