In the figure below are two current loops, [tex]I_1[/tex] and [tex]I_2[/tex]. Determine the following:

a) If [tex]I_1 = I_2[/tex], find the direction and total magnetic field ([tex]B[/tex] field) at the center of the diagram. Use three significant figures for your answer. Given values: [tex]I_1 = 3.47 \, \text{A}[/tex], [tex]R_1 = 1.0 \, \mu \text{m}[/tex], [tex]R_2 = \frac{3}{2}R_1[/tex], [tex]R_3 = \frac{1}{2}R_1[/tex], [tex]R_4 = 2R_1[/tex], [tex]R_5 = \frac{5}{2}R_1[/tex]. (Hint: Circle)

b) If [tex]I_1 = 59.1 \, \text{A}[/tex] and [tex]I_2 = \frac{1}{2} I_1[/tex], find the direction and total magnetic field ([tex]B[/tex] field) at the center of the diagram. Use three significant figures for your answer. Given values: [tex]R_1 = 1.0 \, \mu \text{m}[/tex], [tex]R_2 = \frac{3}{2}R_1[/tex], [tex]R_3 = \frac{1}{2}R_1[/tex], [tex]R_4 = 2R_1[/tex], [tex]R_5 = \frac{5}{2}R_1[/tex]. (Hint: Title of this class)

Each part is worth 15 points.

As before, the direction of the B field in the center will be determined by the direction of the currents. Since I2 = 1/2 I1, the magnetic field created by I2 will be half the magnitude of the magnetic field created by I1. The direction of the B field created by I1 will be out of the page, while the direction of the B field created by I2 will also be out of the page

As the Brainly AI Helper, I'll be happy to assist you with your question.

a) To determine the direction and total magnetic field (B field) in the center of the diagram when I1 = I2, we can use the concept of the Biot-Savart law.

The Biot-Savart law states that the magnetic field at a point due to a current-carrying wire is directly proportional to the current and inversely proportional to the distance from the wire.

1. First, let's consider the direction of the B field in the center. Since I1 = I2, the two currents will create magnetic fields that are equal in magnitude but opposite in direction. The magnetic field created by I1 will be directed out of the page (towards you), while the magnetic field created by I2 will be directed into the page (away from you).

2. Next, let's calculate the total B field in the center. Since the two currents are equal and opposite, their magnetic fields will cancel each other out at the center. Therefore, the total B field in the center will be zero.

b) Now, let's determine the direction and total B field in the center of the diagram when I1 = 59.1A.

2. To calculate the total B field in the center, we need to consider the magnetic fields due to both currents. Since they have the same direction and magnitude, we can simply add them together. Therefore, the total B field in the center will be twice the magnitude of the magnetic field created by I1 (or I2).

I hope this helps! Let me know if you have any further questions.

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