As shown in the figure two loops carry currents with I1 = 3.6 A and I2 =9.4 A. The radii r1 = 12.5 cm and r2 = 18.5 cm. If a long current carrying wire is placed at point A parallel to Y axis, find the magnetic field at the origin. The long straight wire carries 10A of current in the upwards. Answer is 2.46*10^-5T out of page
s.yimg.com/tr/i/4b6cdcfc391f49838154b16d1c0f19a8_A.png
To find the magnetic field at the origin due to the current carrying wire at point A, we can use the Biot-Savart law. The Biot-Savart law states that the magnetic field created by a long straight wire is proportional to the current flowing through the wire and inversely proportional to the distance from the wire.
Here are the steps to calculate the magnetic field at the origin:
1. Determine the magnitude of the magnetic field at the origin due to each loop separately:
- For loop 1: The formula to calculate the magnetic field produced by a loop of current is B1 = (μ0 * I1 * r1^2) / (2 * (r1^2 + x^2)^(3/2)), where μ0 is the permeability of free space (4π × 10^-7 T m/A), I1 is the current in loop 1, r1 is the radius of loop 1, and x is the distance from the center of the loop to the point of interest (in this case, the origin). Plug in the values and calculate B1.
- For loop 2: Use the same formula as above, but replace I1 with I2 and r1 with r2 to calculate B2.
2. Calculate the magnetic field at the origin due to the current-carrying wire at point A by summing up the contributions from each loop:
B_total = B1 + B2
3. Determine the direction of the magnetic field at the origin:
Looking at the figure, since the current in the wire at point A is directed in the upwards direction, the magnetic field produced by this wire will be pointing out of the page.
4. Finally, plug in the given values of I1, I2, r1, r2, and calculate the magnetic field at the origin by adding B1 and B2. The answer should be 2.46 * 10^-5 T, out of the page.
Note: Make sure to convert the distances from centimeters to meters, if necessary, for consistent unit calculations.