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在扭曲的2D磁体中直接可视化磁域和摩尔磁

  • 0Department of Physics, University of Washington, Seattle, WA 98195, USA.
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Magnetic Field Lines 01:19

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The representation of magnetic fields by magnetic field lines is very useful in visualizing the strength and direction of the magnetic field. Each of the magnetic field lines forms a closed loop. The field lines emerge from the north pole (N), loop around to the south pole (S), and continue through the bar magnet back to the north pole.
Magnetic field lines follow several hard-and-fast rules:

The direction of the magnetic field is tangent to the field line at any point in space. A small...

Magnetic Field Due to Two Straight Wires 01:18

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Consider two parallel straight wires carrying a current of 10 A and 20 A in the same direction and separated by a distance of 20 cm. Calculate the magnetic field at a point "P2", midway between the wires. Also, evaluate the magnetic field when the direction of the current is reversed in the second wire.

The current flowing in the wires and the separation distance between the wires are the known quantities. The magnetic field at a point 10 cm from each wire must be evaluated.
The magnetic field...

Divergence and Curl of Magnetic Field 01:26

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The magnetic field due to a volume current distribution given by the Biot–Savart Law can be expressed as follows:

To evaluate the divergence of the magnetic field, the divergence is applied to both sides of the Biot–Savart equation:

Applying the vector product rule, the term within the integral is simplified to the following equation:

The first term involving the curl of the current density function is zero since the current density is independent of the field coordinates. Using...

Magnetic Field due to Moving Charges 01:23

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A stationary charge creates and interacts with the electric field, while a moving charge creates a magnetic field.
Consider a point charge moving with a constant velocity. Like the electric field, the magnetic field at any point is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance between the source point and the field point. However, unlike the electric field, the magnetic field is always perpendicular to the plane containing the line...

Magnetic Field Of A Current Loop 01:16

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Consider a circular loop with a radius a, that carries a current I. The magnetic field due to the current at an arbitrary point P along the axis of the loop can be calculated using the Biot-Savart law.

Let axial point P be a distance x from the center of the loop. The magnetic field at P, produced by an infinitesimal current element dl, is directed at an angle θ. The current element and the unit vector along the line joining P are perpendicular at all points on the loop. Substituting this and...

Magnetic Field Due To A Thin Straight Wire 01:28

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Consider an infinitely long straight wire carrying a current I. The magnetic field at point P at a distance a from the origin can be calculated using the Biot-Savart law.

Consider a current element dx at a distance x from the origin. The current element makes an angle θ with the line joining dx and P. Using the Pythagorus theorum to express the distance between the current element and the point, the magnetic field due to the current element at point P can be estimated using Equation 1.

The...