Magnetic Field around a Circular Wire
Circular wire produces magnetic field inside the circle and outside the circle. Magnetic field around a circular wire is calculated by the formula;
B=2πk.i/r
![](https://lh3.googleusercontent.com/-pNS3gGs6RbU/VpfG2b6FSFI/AAAAAAAALHM/MoPEPQdsXbU/s251-Ic42/1.png)
Direction of the magnetic field at the center of the circle is found with right hand rule.
![](https://lh3.googleusercontent.com/-qM4lxlb7Ews/VpfG2X0T47I/AAAAAAAALG0/LG7FUnLHjZk/s265-Ic42/2.png)
Your thumb shows the direction of magnetic field and four fingers show direction of current. Moreover, we can show the direction of current inside the circle with following pictures;
![](https://lh3.googleusercontent.com/-PSJZMTy1Wr4/VpfG2Y_dAUI/AAAAAAAALHw/1Hy5BTKVe-s/s502-Ic42/3.png)
Example: Find the magnitude and direction of magnetic field at the center of the semicircle given below.
![](https://lh3.googleusercontent.com/-07X3mInQzGU/VpfG2x5ESCI/AAAAAAAALH0/2md1QvES9lE/s421-Ic42/4.png)
When we apply right hand rule we see that direction of magnetic field is inward to the page as shown in the picture below, since we have semicircle, we put 1/2 in front of our formula;
![](https://lh3.googleusercontent.com/-Ow5eGjAd8hY/VpfG3NG6cwI/AAAAAAAALHs/3eSZmLGn1ck/s449-Ic42/5.png)
Example: Directions of i1 and i2 currents are opposite. If the magnetic field at the center of the circles is zero find the ratio of i1 to i2 i1/i2?
![](https://lh3.googleusercontent.com/-J6I1nCWj4eI/VpfG3dlHnxI/AAAAAAAALHk/EyHU_ntoxPE/s165-Ic42/6.png)
Smaller circle has magnetic field ;
![](https://lh3.googleusercontent.com/-aYt6FzJIImc/VpfG3nAoT_I/AAAAAAAALHo/rUO3sKh5aWc/s572-Ic42/7.png)
Example: Find the magnetic field produced by currents i1 and i2 at point O.
![](https://lh3.googleusercontent.com/-AmFKcrEUERk/VpfG3x8NAPI/AAAAAAAALIA/oPyAt2wwm2c/s277-Ic42/8.png)
If we apply right hand rule, directions of currents are;
i1:inward
i2:outward
Thus, total magnetic field at point O becomes the difference of these magnetic fields.
![](https://lh3.googleusercontent.com/-PYrz0jhck1k/VpfG3wd1R4I/AAAAAAAALH4/YLX9R7FIK-c/s470-Ic42/9.png)
0 comments:
Post a Comment