A current- carrying straight wire is kept along the axis of a circular loop carrying a current. The straight wire

Options

A. will exert an inward force on the circular loop
B. will exert an outward force on the circular loop
C. will not exert any force on the circular loop
D. will exert a force on the circular loop parallel to itself.

Answer

To solve the problem of a current-carrying straight wire placed along the axis of a circular loop carrying a current, we can follow these steps:

### Step 1: Understand the Configuration
We have a circular loop with a current flowing through it, and a straight wire also carrying a current is positioned along the axis of the loop.

### Step 2: Determine the Magnetic Field Due to the Straight Wire
The magnetic field (B) created by a long straight wire carrying current (I) at a distance (r) from the wire is given by the formula:
\[ B = \frac{\mu_0 I}{2\pi r} \]
where \(\mu_0\) is the permeability of free space.

### Step 3: Analyze the Magnetic Field Direction
Using the right-hand rule, we can determine the direction of the magnetic field produced by the straight wire. If the current in the wire flows in a certain direction, the magnetic field will circulate around the wire in a direction determined by the right-hand rule.

### Step 4: Calculate the Force on the Circular Loop
The force (F) on a segment of the circular loop due to the magnetic field created by the straight wire can be calculated using the formula:
\[ F = BIL \sin \theta \]
where:
- B is the magnetic field due to the straight wire,
- I is the current in the circular loop,
- L is the length of the segment of the loop in the magnetic field,
- \(\theta\) is the angle between the direction of the current in the loop and the magnetic field.

### Step 5: Determine the Angle \(\theta\)
In this case, since the straight wire is along the axis of the circular loop, the angle \(\theta\) between the magnetic field produced by the straight wire and the current in the loop is 0 degrees. Therefore:
\[ \sin \theta = \sin 0 = 0 \]

### Step 6: Calculate the Force
Substituting \(\sin \theta = 0\) into the force equation:
\[ F = BIL \cdot 0 = 0 \]
This indicates that there is no force exerted on the circular loop by the straight wire.

### Conclusion
The straight wire will not exert any force on the circular loop carrying current.

### Final Answer
The answer to the question is option C: The straight wire will not exert any force on the circular loop.

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