kasse said:I also have a problem with this task:
http://www.badongo.com/pic/3641364
In a) I'm asked to show that the expression for B in P is correct, which I have made.
In b) the loop is replaced by a short coil with N loops. The direction of the current is the same. I'm asked to find
- the magnetic field in the center of the coil, and
- in what distance along the y-axis from the center of the coil is the B field reduced to 1/3 of it's maximal.
I use this formula to find the magnetic field in the center: B*L = N*(mju)*I --> B = N*(mju)*I/L
The answer is the same as in my book, except that L is replaced with 2R. Why is this? If the coil is short, it's length should definitely not be 2L!
alphysicist said:Hi kasse,
Here you want to think of the coils as being so short that the coils are effectively on top of one another. You can find the field of one loop at its center by using the result from part a; what is the value of y at the center of the loop? Then the magnetic field of N loops would just add together. Do you get the result?
The Biot-Savart law is a fundamental principle in electromagnetism that describes the magnetic field generated by a steady current in a conductor. It states that the magnetic field at a certain point is directly proportional to the current, the length of the conductor, and the sine of the angle between the current and the line connecting the point to the conductor.
The Biot-Savart law is used to calculate the magnetic field produced by a current in a conductor. It is a crucial tool in understanding the behavior of magnets, electric motors, and other devices that rely on magnetic fields.
A quarter loop example of the Biot-Savart law is a simplified scenario in which a quarter of a circle is used to represent a current-carrying wire. This allows for easier calculation of the magnetic field at a specific point compared to more complex shapes.
The quarter loop example demonstrates the Biot-Savart law by showing how the magnetic field strength at a point changes as the angle between the current and the point changes. It also illustrates how the distance from the point to the conductor affects the strength of the magnetic field.
The Biot-Savart law has many real-life applications, including in the design of electric motors, generators, and transformers. It is also used in medical imaging techniques such as magnetic resonance imaging (MRI) and in the study of Earth's magnetic field. Additionally, it is used in the development of new technologies such as magnetic levitation trains and magnetic storage devices.