29.13
Toroiden
Ein Toroid ist eine eng gewundene donutförmige Spule, die mit einem einzigen leitenden Draht konstruiert wird. Im Allgemeinen wird angenommen, dass ei…
A straight solenoid bent in the form of a doughnut-shaped coil is called a toroid.
A toroid can be assumed as an aggregate of circular loops perpendicular to its axis. The magnetic field lines are circular and concentric to the toroid axis.
If the fingers of the right hand curl in the current direction, the thumb points to the magnetic field direction.
Consider a circular Amperian loop inside the toroid. The magnetic field along this loop has constant magnitude and is tangential to the path.
Now, applying Ampere's Law, the line integral of the magnetic field equals the product of the magnetic field and the circumference of the loop.
The net enclosed current in the loop equals the total number of turns times the current.
Thus, the obtained magnetic field inside a toroid varies inversely with the distance from its axis.
The magnetic field inside the hollow circle is zero since it does not enclose any current.
Outside the toroid, the currents flowing in opposite directions cancel each other out. Hence, the magnetic field is zero.
View the full transcript and gain access to JoVE Core videos
Q1: What is a toroid and how is it constructed?
A toroid is a doughnut-shaped coil made by bending a straight solenoid into a circular form using a single conducting wire. It consists of multiple circular loops perpendicular to its axis, tightly wound together. When current flows through the toroid, it generates a magnetic field with field lines that are circular and concentric to the toroid's axis.
Q2: How do you determine the direction of the magnetic field in a toroid?
Use the right-hand rule to find the magnetic field direction in a toroid. Curl the fingers of your right hand in the direction of current flow around the toroid. Your thumb then points in the direction of the magnetic field lines, which are circular and concentric to the toroid's axis.
Q3: Why is the magnetic field zero inside the hollow center of a toroid?
The magnetic field inside the hollow circle of a toroid is zero because the Amperian loop drawn there does not enclose any current. Since Ampere's Law relates the magnetic field to the enclosed current, a loop with no enclosed current produces zero magnetic field in that region.
Q4: What happens to the magnetic field outside a toroid?
The magnetic field outside a toroid is zero because the currents flowing in opposite directions in adjacent turns cancel each other out. The net effect of these opposing currents results in no magnetic field in the external region surrounding the toroid.
Q5: How does the magnetic field inside a toroid vary with distance from its axis?
The magnetic field inside a toroid varies inversely with the distance from its axis. Using Ampere's Law, the magnetic field strength decreases as you move farther from the center. This inverse relationship means the field is strongest near the inner edge and weakest near the outer edge of the toroid.
Q6: How do you calculate the number of turns needed in a toroid for a specific magnetic field?
Use the magnetic field formula for a toroid, which relates the number of turns to the current, distance from the axis, and desired magnetic field strength. By rearranging the formula and substituting known values such as inner radius, outer radius, current, and target magnetic field, you can solve for the required number of turns.
Q7: Why can a toroid be modeled as an aggregate of circular loops?
A toroid can be modeled as an aggregate of circular loops perpendicular to its axis because it is constructed by winding a single wire into many turns around a circular core. Each turn forms a circular loop, and treating the toroid as a collection of these loops simplifies the analysis of its magnetic field using Ampere's Law and symmetry arguments.