A square current carrying loop is suspended in a uniform magnetic field acting in the plane of the loop. If the force on one arm of the loop is `vec(F)`, the net force on the remaining three arms of the loop is

Options

A. `3 vec(F)`
B. `-vec(F)`
C. `-3 vec(F)`
D. `vec(F)`

Explanation

To solve the problem, we need to analyze the forces acting on a square current-carrying loop suspended in a uniform magnetic field. Here’s a step-by-step breakdown of the solution:

### Step 1: Understanding the Setup
A square current-carrying loop is placed in a uniform magnetic field that is acting in the plane of the loop. The magnetic field exerts forces on the sides of the loop due to the current flowing through it.

**Hint:** Visualize the loop and the direction of the magnetic field to understand how forces will act on each arm of the loop.

### Step 2: Force on One Arm
According to the problem, the force on one arm of the loop is given as \( \vec{F} \). The force on a current-carrying conductor in a magnetic field is given by the formula:
\[ \vec{F} = I \, \vec{L} \times \vec{B} \]
where \( I \) is the current, \( \vec{L} \) is the length vector of the conductor, and \( \vec{B} \) is the magnetic field.

**Hint:** Remember that the direction of the force is determined by the right-hand rule applied to the cross product.

### Step 3: Net Force on the Loop
For a closed loop in a uniform magnetic field, the net force on the entire loop can be calculated by summing the forces on each arm. However, since the magnetic field is uniform, the forces on opposite arms will be equal in magnitude and opposite in direction, leading to a net force of zero on the entire loop.

**Hint:** Consider the symmetry of the loop and how forces on opposite sides cancel each other out.

### Step 4: Analyzing the Remaining Three Arms
If one arm experiences a force \( \vec{F} \), the forces on the other three arms must balance this out to maintain the net force of the loop at zero. Therefore, the net force on the remaining three arms must be equal in magnitude but opposite in direction to the force on the one arm.

Thus, the net force on the remaining three arms is:
\[ \text{Net Force on remaining three arms} = -\vec{F} \]

**Hint:** Think about how forces must balance in a closed system to maintain equilibrium.

### Conclusion
The net force on the remaining three arms of the square current-carrying loop is \( -\vec{F} \).

### Final Answer
The net force on the remaining three arms of the loop is \( -\vec{F} \).

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