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  • 0Department of Chemical Engineering, Columbia University, New York, NY, USA. kyle.bishop@columbia.edu.

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Magnetic Field due to Moving Charges 01:23

9.2K

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

5.0K

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...

Torque On A Current Loop In A Magnetic Field 01:13

4.7K

The most common application of magnetic force on current-carrying wires is in electric motors. These consist of loops of wire, which are placed between the magnets with a magnetic field. When current flows through the loops, the magnetic field applies torque, which causes the shaft to rotate, thus converting electrical energy to mechanical energy.
Consider a rectangular current-carrying loop containing N turns of wire, placed in a uniform magnetic field. The net force on a current-carrying loop...

Force On A Current Loop In A Magnetic Field 01:17

3.3K

Magnetic forces on wires carrying current are most frequently applied in motors. A DC motor is a device that converts electrical energy into mechanical work. In motors, wire loops are enclosed in a magnetic field. When current flows through the loops, the magnetic field applies torque, which causes the shaft to rotate. The direction of the current is reversed once the loop's surface area is lined up with the magnetic field, causing a constant torque on the loop. During the process,...

Magnetic Vector Potential 01:15

782

In electrostatics, the electric field can be written as the negative gradient of the potential. In magnetostatics, the zero divergence of the magnetic field ensures that the magnetic field can be expressed as the curl of a vector potential. This potential is known as the magnetic vector potential.
Consider an ideal solenoid with n turns per unit length and radius R. If I is the current through the solenoid, the magnetic field inside the solenoid is expressed as the product of vacuum...

Magnetic Field Due to Two Straight Wires 01:18

2.9K

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...