Magnetic Field For A Straight Conductor And Ampere'S Law - Ampeir Law

Magnetic Field For A Straight Conductor And Ampere’s Law - Ampeir Law

Slide 1:

The magnetic field is the region in which a magnetic force is experienced due to the presence of a magnet or a current-carrying conductor.
Ampere’s Law describes the relationship between the magnetic field and the current flowing through a conductor.

Slide 2:

The value of the magnetic field depends on the current passing through the conductor.
For a straight conductor, we can calculate the magnetic field using Ampere’s Law.

Slide 3:

Ampere’s Law states that the magnetic field around a closed loop is directly proportional to the current passing through the loop.
Mathematically, it can be represented as:
- ∫ B · dl = μ₀ * I

Slide 4:

In the above equation, ∫ B · dl represents the line integral of the magnetic field along the closed loop.
μ₀ is the permeability of free space, which has a value of 4π × 10⁻⁷ T m/A.
I is the current passing through the loop.

Slide 5:

Using Ampere’s Law, we can determine the magnetic field at a specific distance from a straight conductor with a known current.
The magnitude of the magnetic field can be calculated using the equation:
- B = (μ₀ * I) / (2πr)

Slide 6:

In the above equation, B represents the magnetic field strength.
μ₀ is the permeability of free space.
I is the current passing through the conductor.
r is the distance from the conductor.

Slide 7:

The direction of the magnetic field lines around a straight conductor can be determined using the right-hand thumb rule.
Wrap your right hand around the conductor in the direction of the current. The direction in which your thumb points gives the direction of the magnetic field.

Slide 8:

Let’s consider an example: A straight conductor carries a current of 5 A. What is the magnetic field at a distance of 10 cm from the conductor?
Using the equation B = (μ₀ * I) / (2πr), we can calculate the magnetic field.

Slide 9:

Solution:
- Given: I = 5 A, r = 10 cm = 0.1 m
- Using B = (μ₀ * I) / (2πr),
- B = (4π × 10⁻⁷ T m/A * 5 A) / (2π * 0.1 m)
- B = (2 × 10⁻⁶ T) / (0.2 m)
- B = 10⁻⁵ T

Slide 10:

Therefore, the magnetic field at a distance of 10 cm from the conductor is 10⁻⁵ T.
This implies that at this point, a magnetic force of 10⁻⁵ N will be experienced per unit charge moving perpendicular to the current.

Slide 11:

A current-carrying loop or coil of wire also produces a magnetic field.
The magnetic field produced by a coil is cumulative due to the individual contributions from each segment of the wire.

Slide 12:

For a solenoid (cylindrical coil of wire), the magnetic field inside is nearly constant and parallel to the axis of the coil.
The magnetic field lines are tightly packed inside the solenoid.

Slide 13:

The strength of the magnetic field inside a solenoid depends on the number of turns per unit length and the current flowing through the solenoid.
The magnetic field inside a solenoid can be calculated using the equation:
- B = μ₀ * n * I

Slide 14:

In the above equation, B represents the magnetic field strength.
μ₀ is the permeability of free space.
n is the number of turns per unit length (also known as the coil density).
I is the current passing through the solenoid.

Slide 15:

Let’s consider an example: A solenoid has 500 turns per meter and carries a current of 2 A. Calculate the magnetic field inside the solenoid.
Using the equation B = μ₀ * n * I, we can find the value of the magnetic field.

Slide 16:

Solution:
- Given: n = 500 turns/m, I = 2 A
- Using B = μ₀ * n * I,
- B = (4π × 10⁻⁷ T m/A) * (500 turns/m) * (2 A)
- B = 4π × 10⁻⁷ * 500 * 2 T
- B = 4π × 10⁻⁷ * 1000 T
- B = 4π × 10⁻⁴ T

Slide 17:

Therefore, the magnetic field inside the solenoid is 4π × 10⁻⁴ T.
This implies that at any point inside the solenoid, the magnetic force acting on a unit charge moving perpendicular to the current is 4π × 10⁻⁴ N.

Slide 18:

It’s important to note that the coiled structure of a solenoid allows it to act like a magnet when a current flows through it.
The strength of the electromagnet (or solenoid) can be increased by increasing the number of turns or by using a material with higher magnetic permeability.

Slide 19:

The cumulative magnetic field inside a solenoid can be seen as the sum of the individual magnetic fields created by each turn of the wire.
This results in strong and uniform magnetic field lines within the solenoid.

Slide 20:

The concept of a solenoid is widely used in various applications, including electric motors, speakers, magnetic resonance imaging (MRI) machines, and magnetic levitation systems.
Understanding the magnetic field produced by a solenoid is essential for analyzing and designing such systems.

The strength of the magnetic field around a straight conductor decreases as the distance from the conductor increases.
This follows an inverse square relationship, similar to the electrical field.

The magnetic field produced by a straight conductor is circular in shape and perpendicular to the direction of the current.
The field lines form concentric circles around the conductor.

The direction of the magnetic field can be determined using the right-hand thumb rule.
Point your thumb in the direction of the current and the curled fingers will indicate the direction of the magnetic field.

The magnetic field produced by a straight conductor is not affected by the length of the conductor but depends only on the current passing through it.

The magnetic field produced by multiple straight conductors can be determined by considering the contributions of each conductor individually and adding them vectorially.

The direction of the magnetic field depends on the direction of the current flowing through the conductors.
For parallel conductors carrying current in the same direction, the magnetic field lines are additive between the conductors.

For parallel conductors carrying current in opposite directions, the magnetic field lines are subtractive between the conductors.
The magnetic field between them is weaker compared to the magnetic field further away from the conductors.

The magnetic field produced by a current-carrying conductor can exert a force on other current-carrying conductors placed in its proximity.
This phenomenon is known as magnetic interaction or magnetic induction.

Magnetic interactions between current-carrying conductors can be used in various applications such as transformers, electric motors, and generators.

Understanding the magnetic field produced by a straight conductor and the principles of Ampere’s Law is crucial for solving problems related to magnetic fields and electromagnetism.
Practicing numerical problems and analyzing real-life applications can further strengthen your understanding of this topic.