Slide 2:

• A straight conductor carrying a current produces a magnetic field around it.
• The magnetic field lines form concentric circles around the conductor.
• The direction of the magnetic field can be determined using the right-hand rule.

Slide 3:

• Ampere’s Law relates the magnetic field around a closed loop to the current passing through the loop.
• The mathematical form of Ampere’s Law is:
  • ∮ B · dl = μ₀Ienc
  • B is the magnetic field
  • dl represents an infinitesimal element of the closed loop
  • Ienc is the total current enclosed by the loop
  • μ₀ is the permeability of free space

Slide 4:

• Ampere’s Law can be used to calculate the magnetic field produced by a long straight conductor.
• Consider a long straight conductor carrying a current I.
• We create a circular loop of radius r around the conductor.
• The current passing through the loop is Ienc = I.
• Applying Ampere’s Law, we find:
  • B ∮ dl = μ₀I
  • B × 2πr = μ₀I
  • B = (μ₀I) / (2πr)

Slide 5:

• The magnetic field produced by a straight conductor decreases with increasing distance from the conductor.
• The magnetic field lines near the conductor are closer together, indicating a stronger magnetic field.
• The magnetic field lines become more spread out as the distance from the conductor increases.

Slide 6:

• The direction of the magnetic field around a conductor can be determined using the right-hand rule.
• Align your right thumb in the direction of the current.
• Your fingers will curl around the conductor in the direction of the magnetic field.

Slide 7:

Example:

• Consider a straight conductor with a current of 5 A.
• Calculate the magnetic field at a distance of 10 cm from the conductor. Solution:
• Using the formula B = (μ₀I) / (2πr), we have:
  • B = (4π × 10^-7 T m/A)(5 A) / (2π × 0.10 m)
  • B ≈ 0.628 × 10^-6 T

Slide 8:

• The SI unit of magnetic field is Tesla (T).
• 1 Tesla is equivalent to 1 N/(A·m), which means 1 Tesla exerts a force of 1 Newton on a wire carrying a current of 1 Ampere per meter in a direction perpendicular to the magnetic field.

Slide 9:

• The magnitude of the magnetic field produced by a straight conductor decreases with the inverse of the distance from the conductor.
• This behavior is similar to the electric field of a point charge.

Slide 10:

• Ampere’s Law can also be used to calculate the magnetic field produced by a straight conductor with a varying current or a combination of multiple conductors.
• It provides a powerful tool for understanding and analyzing electromagnetic phenomena.

Magnetic Field for a Current-Carrying Conductor - Infinite Long Straight Conductor

• An infinite long straight conductor carrying current produces a magnetic field that is uniform in magnitude and direction.
• The magnitude of the magnetic field at any point perpendicular to the conductor can be calculated using Ampere’s Law.
• The formula for the magnitude of the magnetic field is B = (μ₀I) / (2πr), where I is the current and r is the perpendicular distance from the conductor.

Slide 12:

• Consider a long straight conductor carrying a current I.
• The magnetic field produced by this conductor is not affected by the length of the conductor.
• As long as the distance r is large compared to the dimensions of the conductor, the magnetic field is approximately constant.

Slide 13:

• The magnetic field lines around an infinite straight conductor form concentric circles oriented perpendicularly to the conductor.
• The direction of the magnetic field lines can be determined using the right-hand rule.
• The magnetic field lines are closed loops, indicating the existence of a magnetic field around the conductor.

Slide 14:

• The magnetic field lines around an infinite long straight conductor are equidistant and have the same magnitude at any perpendicular distance from the conductor.
• The strength of the magnetic field decreases with distance from the conductor according to the formula B = (μ₀I) / (2πr).

Slide 15:

Example:

• Consider an infinite long straight conductor carrying a current of 10 A.
• Calculate the magnetic field at a distance of 5 cm from the conductor. Solution:
• Using the formula B = (μ₀I) / (2πr), we have:
  • B = (4π × 10^-7 T m/A)(10 A) / (2π × 0.05 m)
  • B ≈ 3.182 × 10^-5 T

Slide 16:

• The magnetic field produced by an infinite long straight conductor can be used in various applications, such as magnetic compasses and electromagnets.
• It is important to note that the formula for the magnetic field assumes there is no other nearby magnetic field that could interfere with the ideal configuration.

Slide 17:

• The direction of the magnetic field produced by an infinite long straight conductor can be determined using the right-hand rule.
• The right-hand rule states that if you point the thumb of your right hand in the direction of the current, your fingers will curl in the direction of the magnetic field.

Slide 18:

• When two infinite long straight conductors are parallel to each other, carrying currents in the same direction, the magnetic fields produced by the conductors interact.
• The magnetic field due to one conductor influences the other conductor and vice versa.
• The magnetic field lines become concentric toroidal shells around the combined conductors.

Slide 19:

• When two infinite long straight conductors are parallel to each other, carrying currents in opposite directions, the magnetic fields produced by the conductors interact in a different way.
• The magnetic field lines between the conductors cancel out, while outside the conductors, the fields combine to form a uniform field in the opposite direction to the individual magnetic fields.

Slide 20:

• The interaction of magnetic fields produced by infinite long straight conductors is an important concept in electromagnetism.
• It can be used to understand and predict the behavior of current-carrying conductors and circuits.

Slide 21:

• Infinite loop of straight current-carrying conductor means a conductor forming a closed loop where the current flows in the same direction throughout.
• The magnetic field produced by an infinite loop of straight current-carrying conductor follows the same pattern as that of an infinite long straight conductor.
• The magnetic field lines form concentric circles around the loop, perpendicular to the loop plane.

Slide 22:

• The magnitude of the magnetic field at any point along the axis of the loop can be calculated using Ampere’s Law.
• Ampere’s Law states that the integral of the magnetic field along a closed loop is equal to the product of the permeability of free space and the total current passing through the loop.
• For an infinite loop of straight current, the formula for the magnetic field is given by B = (μ₀I) / (2R), where I is the current and R is the radius of the loop.

Slide 23:

• The direction of the magnetic field produced by an infinite loop of straight current-carrying conductor can be determined using the right-hand rule.
• Wrap your fingers around the loop in the direction of the current, and your thumb will point in the direction of the magnetic field inside the loop.

Slide 24:

Example:

• Consider an infinite loop of straight current-carrying conductor with a radius of 0.2 m, carrying a current of 3 A.
• Calculate the magnetic field at a point along the axis of the loop, located at a distance of 0.1 m from the center of the loop. Solution:
• Using the formula B = (μ₀I) / (2R), we have:
  • B = (4π × 10^-7 T m/A)(3 A) / (2 × 0.2 m)
  • B ≈ 9.55 × 10^-6 T

Slide 25:

• The magnetic field produced by an infinite loop of straight current-carrying conductor is strongest at the center of the loop.
• As we move away from the center along the axis of the loop, the magnetic field decreases with the inverse of the distance from the center.

Slide 26:

• The magnetic field produced by an infinite loop of straight current-carrying conductor is zero at the center of the loop.
• This is because the magnetic fields produced by different segments of the loop cancel each other out at the center.

Slide 27:

• The magnetic field lines inside the loop of an infinite loop of straight current-carrying conductor are perpendicular to the loop plane.
• The magnetic field lines become more spread out as we move away from the loop.

Slide 28:

• The magnetic field produced by an infinite loop of straight current-carrying conductor can be used in various applications, such as inductive heating, magnetic resonance imaging (MRI), and magnetic levitation.

Slide 29:

• The interaction between the magnetic fields produced by two or more infinite loops of straight current-carrying conductors can be complex and depends on various factors, such as the direction and magnitude of the current in each loop and the spatial arrangement of the loops.
• The principles of superposition can be applied to calculate the resultant magnetic field in such cases.

Slide 30:

• Understanding the magnetic field produced by straight current-carrying conductors and applying Ampere’s Law is crucial for analyzing and designing electrical circuits and devices.
• This knowledge also forms the foundation for the study of more advanced topics in electromagnetism and related fields.