Understanding Magnetic Field Intensity and Force

The question asks about a physical unit that defines the intensity of a field based on the force it exerts on a current-carrying conductor. This relates directly to the concept of a magnetic field and the Lorentz force experienced by charges moving within it, which results in a force on a conductor carrying a current.

Force on a Current-Carrying Conductor

When a conductor of length \(L\) carrying a current \(I\) is placed in a magnetic field with magnetic flux density \(B\), it experiences a force. For the specific case where the conductor is perpendicular to the magnetic field, the magnitude of the force \(F\) is given by the formula:

\(F = BIL\)

Here:

• \(F\) is the force acting on the conductor (measured in Newtons, N).
• \(B\) is the magnetic flux density or magnetic field intensity (the unit we need to find).
• \(I\) is the current flowing through the conductor (measured in Amperes, A).
• \(L\) is the length of the conductor within the magnetic field (measured in meters, m).

Deriving the Unit of Magnetic Field Intensity

We can rearrange the formula \(F = BIL\) to solve for \(B\):

\(B = \frac{F}{IL}\)

Now, let's substitute the standard SI units for force, current, and length into this equation:

Unit of \(B\) = \(\frac{\text{Unit of } F}{\text{Unit of } I \times \text{Unit of } L} = \frac{\text{Newtons}}{\text{Amperes} \times \text{meters}}\)

So, the unit of magnetic field intensity is \(\frac{\text{N}}{\text{A} \cdot \text{m}}\).

The question describes a field intensity that produces one newton (N) of force per ampere (A) per meter (m) of conductor. This matches the unit \(\frac{\text{N}}{\text{A} \cdot \text{m}}\).

Identifying the Physical Unit

We need to find which of the given options corresponds to the unit \(\frac{\text{N}}{\text{A} \cdot \text{m}}\). Let's look at the options:

• Candela (cd): This is the SI base unit of luminous intensity. It is unrelated to magnetic fields or force on conductors.
• Coulomb (C): This is the SI unit of electric charge. It is also unrelated to magnetic field intensity.
• Tesla (T): The Tesla is the SI derived unit of magnetic flux density (\(B\)). By definition, one Tesla is equal to one Newton per ampere-meter (\(1\text{ T} = 1\frac{\text{N}}{\text{A} \cdot \text{m}}\)). This perfectly matches the description in the question.
• Pascal (Pa): This is the SI derived unit of pressure, defined as one Newton per square meter (\(1\text{ Pa} = 1\frac{\text{N}}{\text{m}^2}\)). It is unrelated to magnetic field intensity.

Based on the definition and unit derivation, the physical unit that fits the description is the Tesla.

Summary of Units

Here's a quick look at the units mentioned:

The description provided in the question, "field intensity that produces one newton (N) of force per ampere (A) per meter of conductor," is the definition of the Tesla.

Revision Table: Electromagnetic Units

Additional Information: Magnetic Field and Force

The magnetic field is a region around a magnetic material or a moving electric charge within which the force of magnetism acts. Magnetic flux density, measured in Teslas, is a measure of the strength of this magnetic field.

The force on a current-carrying conductor in a magnetic field is a fundamental principle behind electric motors. The force causes a torque on a loop of wire carrying current in a magnetic field, leading to rotational motion.

Another unit sometimes used for magnetic flux density, especially in older texts or different unit systems, is the Gauss (G). The relationship between Tesla and Gauss is \(1\text{ T} = 10^4\text{ G}\). The Tesla is a much larger unit than the Gauss.