#5 (5 points possible)

Two identical solenoids are merged as shown in the figure. Which plot best represents the y-component of the magnetic field as it varies along the x-axis? Treat them as ideal solenoids.

To determine which plot best represents the y-component of the magnetic field as it varies along the x-axis for two identical solenoids merged together, we can use the right-hand rule for solenoids and the principle of superposition.

First, let's review the right-hand rule for solenoids. When you point your right thumb in the direction of the current flowing through the solenoid, your curled fingers indicate the direction of the magnetic field lines inside the solenoid.

Next, let's consider the principle of superposition, which states that the magnetic field produced by multiple sources can be found by adding up the individual magnetic fields produced by each source.

Now, let's analyze the merged solenoids. Since the solenoids are identical, the current flowing through them will be in the same direction. According to the right-hand rule, the magnetic field lines inside each solenoid will form concentric circles around the axis of the solenoids. Therefore, the individual magnetic fields produced by each solenoid will have the same direction along the x-axis.

According to the principle of superposition, when two solenoids merge together, the magnetic fields they produce will add up. Since the magnetic fields of the two solenoids are in the same direction along the x-axis, the resulting magnetic field will also have the same direction along the x-axis.

Based on this analysis, the plot that best represents the y-component of the magnetic field as it varies along the x-axis for the merged solenoids will be a straight line with the same value (positive or negative) for all points on the x-axis. This plot indicates that the y-component of the magnetic field is constant along the x-axis.

(Note: The figure mentioned in the question is not provided, so it's best to rely on the principles and analysis described above to determine the best plot.)