Magnetostatics- Introduction And Biot Savart Law

Magnetostatics: Introduction and Biot-Savart Law

Slide 1:

Magnetostatics is the branch of electromagnetism that studies the magnetic fields and their interactions.
It deals with current-carrying conductors, magnetic fields generated by them, and their effects on charged particles. Slide 2:
Magnetic field lines depict the direction and magnitude of the magnetic field.
They form loops around a current-carrying conductor.
The direction of the magnetic field can be determined using the right-hand thumb rule. Slide 3:
Magnetic field intensity, denoted by H, is the measure of the strength of the magnetic field.
It is defined as the magnetic field strength per unit length of a conductor.
The SI unit of H is ampere-turns per meter (A/m). Slide 4:
Magnetic flux density, denoted by B, is a measure of the strength of the magnetic field at a given point.
It depends on both the magnetic field intensity (H) and the magnetic permeability (μ) of the material.
The SI unit of B is tesla (T). Slide 5:
The Biot-Savart law is used to calculate the magnetic field intensity (H) at a point due to a current-carrying conductor.
It states that the magnetic field intensity at a point is directly proportional to the current (I), the length element (dl), and the sine of the angle between dl and the line joining the point to the element. Slide 6:
Mathematically, the Biot-Savart law is given by:
- H = (μ₀/4π) * (I * dl * sinθ) / r²
- Where H is the magnetic field intensity, μ₀ is the permeability of free space, I is the current, dl is the length element, θ is the angle, and r is the distance from the current element to the point. Slide 7:
Consider a long, straight conductor carrying current I.
To calculate the magnetic field intensity at a point P (distance r from the conductor):
- Divide the conductor into small elements dl.
- Apply the Biot-Savart law to each element and integrate over the entire length of the conductor. Slide 8:
For a circular loop of radius R carrying current I at the center:
The magnetic field intensity at the center of the loop is given by:
- H = (μ₀ * I) / (2R) Slide 9:
Ampere’s circuital law is a mathematical expression of the relationship between magnetic fields and electric currents.
It states that the line integral of the magnetic field intensity (H) around a closed path is equal to the total current passing through the surface bounded by the path. Slide 10:
Mathematically, Ampere’s circuital law is given by:
- ∮H · dl = μ₀ * I
- Where ∮ represents the line integral, H is the magnetic field intensity, dl is a differential length element on the closed path, μ₀ is the permeability of free space, and I is the total current passing through the surface bounded by the path.

Slide 11:

Ampere’s circuital law can be applied to calculate the magnetic field intensity produced by current-carrying conductors with symmetrical geometry.
For example, a straight long conductor produces a magnetic field intensity that varies with distance from the conductor.
Similarly, a circular coil with multiple turns produces a magnetic field intensity that is different at different points. Slide 12:
The magnetic field intensity at the center of a circular coil with multiple turns is given by:
- H = (μ₀ * N * I) / (2R)
- Where N is the number of turns, I is the current, and R is the radius of the coil. Slide 13:
The magnetic field intensity at a point inside a solenoid (a coil with many closely spaced turns) is nearly uniform.
It is given by:
- H = (μ₀ * N * I) / l
- Where N is the number of turns, I is the current, and l is the length of the solenoid. Slide 14:
The magnetic field intensity inside a long, straight, current-carrying conductor is inversely proportional to the distance from the conductor.
The relationship is given by:
- H = (μ₀ * I) / (2πr)
- Where I is the current and r is the distance from the conductor. Slide 15:
Magnetic fields produced by current-carrying conductors exert forces on other current-carrying conductors.
This phenomenon is used in various applications such as magnetic field sensors, motors, and transformers. Slide 16:
The force experienced by a current-carrying conductor in a magnetic field is given by the Lorentz force law.
It states that the force (F) on a conductor of length (L) carrying current (I) is proportional to the magnetic field intensity (H) and the sine of the angle (θ) between the direction of H and the direction of the current. Slide 17:
Mathematically, the Lorentz force law is given by:
- F = I * L * (H x sinθ)
- Where F is the force, I is the current, L is the length of the conductor, H is the magnetic field intensity, and θ is the angle. Slide 18:
The direction of the force on a current-carrying conductor can be determined using the right-hand rule.
Grasp the conductor with your right hand, with the thumb pointing in the direction of the current.
The fingers will curl around in the direction of the magnetic field, and the palm will face the direction of the force. Slide 19:
If a current-carrying conductor is placed in a magnetic field, it experiences a torque.
The torque tends to align the conductor with the magnetic field direction.
This phenomenon is used in devices like galvanometers, electric meters, and electric motors. Slide 20:
The torque experienced by a current loop in a magnetic field is given by:
- τ = N * I * A * B * sinθ
- Where τ is the torque, N is the number of turns, I is the current, A is the area of the loop, B is the magnetic field flux density, and θ is the angle between the normal to the loop and the magnetic field.

Slide 21:

Magnetic field lines inside a bar magnet extend from the north pole to the south pole.
The field lines outside the magnet travel from the south pole to the north pole.
The magnetic field is stronger near the poles and weaker as you move away from them. Slide 22:
The force experienced by a moving charged particle in a magnetic field is given by the equation:
- F = q * v * B * sinθ
- Where F is the force, q is the charge of the particle, v is the velocity of the particle, B is the magnetic field intensity, and θ is the angle between v and B. Slide 23:
The magnetic force on a charged particle moving in a magnetic field always acts perpendicular to the velocity vector.
This force causes the charged particle to move in a circular path or a helical path, depending on the initial conditions. Slide 24:
The radius of the circular path followed by a charged particle in a magnetic field can be determined using the equation:
- r = (m * v) / (q * B)
- Where r is the radius, m is the mass of the particle, v is the velocity of the particle, q is the charge of the particle, and B is the magnetic field intensity. Slide 25:
A charged particle moving along the magnetic field lines experiences no magnetic force.
The force is maximum when the particle moves perpendicular to the magnetic field. Slide 26:
Magnetic field lines never intersect each other.
If they did, it would imply the existence of two different directions for the magnetic field at the same point, which is not possible. Slide 27:
Magnetic field lines are closed loops that emerge from one end of a magnet and return to the other end.
This demonstrates the absence of magnetic monopoles (magnetic poles cannot exist alone; they always come in pairs). Slide 28:
The magnetic field of a permanent magnet arises due to the alignment of the atoms or electrons within it.
The domains in the magnet align in the same direction, resulting in strong magnetic field lines. Slide 29:
Magnetic field lines around a solenoid are similar to those around a bar magnet.
They are shaped like parallel lines inside the solenoid and expand outside the solenoid. Slide 30:
Magnetic fields have a wide range of applications in various devices such as electric motors, generators, transformers, and magnetic resonance imaging (MRI).
They play a crucial role in understanding and manipulating electromagnetism, leading to significant technological advancements.