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Magnetic field due to Toroid / 12th PHYSICS / Magnetism / Meta Gravitation / AMIT KUMAR.
12th PHYSICS / Meta Gravitation / AMIT KUMAR / JEE / NEET/ CUET
Biot-Savart Law quantifies the magnetic field, dB, produced by a small current-carrying element Idl of a conductor at a point at distance r. The law states that dB is proportional to the current (I), the length of the element (dl), the sine of the angle (8) between dl and the line connecting the element to the point, and inversely proportional to the square of the distance (r²) from the ele-ment to the point. The vector form of the law is given by dB = (μ｡/4π) (Idl × f/r²), where µo is the magnetic permeability of free space and f is a unit vector along r.

Key Components and Formula

1. Current Element (IdI): A small, infinitesimal segment of a current-carrying conductor.

2. Observation Point (P): The point in space where the magnetic field is to be calculated. @

3. Distance (r): The distance from the current element to the observation point.

4. Angle (0): The angle between the direction of the current element (dl) and the line joining the element to the observation

Distance (r): The distance from the current element to the observation point.

4. Angle (0): The angle between the direction of the current element (dl) and the line joining the element to the observation point.

5. Permeability of Free Space (μ.): A constant that represents the ability of a vacuum to support the formation of a magnetic field.

The Formula

The magnetic field (dB) produced by the current element can be expressed as:

Magnitude: *dB = (μο/4π) (Idl sine / r²) *

Vector Form: *dB = (μο/4π) (Idl x f/r²) *

Explanation

Proportionality to I and dl: A larger current or a longer conductor element will produce a stronger magnetic field.

Proportionality to sine: The magnetic field is strongest when the current element is perpendicular to the line connecting it to the point (0 = 90°) and is zero when it is parallel

Proportionality to I and dl: A larger current or a longer conductor element will produce a stronger magnetic field.

Proportionality to sine: The magnetic field is strongest when the current element is perpendicular to the line connecting it to the point (0 = 90°) and is zero when it is parallel (0 = 0° or 180°).

Inversely Proportional to r²: The magnetic field decreases rapidly with distance from the source.

Vector Nature: The magnetic field is a vector quantity, and its direction can be found using the right-hand rule. If you point your right thumb in the direction of the current (dl), your curled fingers show the direction of the magnetic field.

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