A flexible wire loop is placed in a uniform external magnetic field if current is passed through wire assuming normal magnetic field. What will be the effect on wire.

Options

A. shape will change
B. shape will not change
C. wire will get straight stretched
D. loop becomes circular parallel to field

Answer

To solve the problem, we need to analyze the effects of a magnetic field on a flexible wire loop carrying current. Here's a step-by-step breakdown of the solution:

### Step 1: Understand the Setup
We have a flexible wire loop placed in a uniform external magnetic field. The magnetic field is assumed to be perpendicular to the plane of the wire loop.

**Hint:** Visualize the wire loop and the magnetic field direction. The magnetic field lines should be drawn perpendicular to the plane of the loop.

### Step 2: Identify the Current Flow
Current is flowing through the wire loop. This current creates a magnetic field around the wire loop, and when placed in an external magnetic field, it will experience a magnetic force.

**Hint:** Remember that the direction of the current is crucial for determining the direction of the magnetic force.

### Step 3: Apply the Right-Hand Rule
To find the direction of the magnetic force acting on the wire, we can use the right-hand rule. Point your thumb in the direction of the current (I) and curl your fingers in the direction of the magnetic field (B). Your palm will then point in the direction of the force (F) acting on the wire.

**Hint:** The right-hand rule is a useful tool for determining the direction of forces in magnetic fields.

### Step 4: Calculate the Force on a Differential Element
Consider a small segment of the wire, \( dl \). The force acting on this segment due to the magnetic field can be expressed as:
\[ F = I \cdot dl \cdot B \cdot \sin(\theta) \]
Since the magnetic field is perpendicular to the current, \( \theta = 90^\circ \) and \( \sin(90^\circ) = 1 \), so:
\[ F = I \cdot dl \cdot B \]

**Hint:** The force on each segment of the wire will be equal and directed outward from the center of the loop.

### Step 5: Analyze the Resultant Force on the Loop
Since the force acts on all segments of the wire loop, it will cause the loop to experience a net outward force. This will tend to change the shape of the loop.

**Hint:** Consider how the forces on different segments interact with each other. The net effect will be a change in shape.

### Step 6: Conclude the Effect on the Wire Loop
As a result of the magnetic forces acting on the wire loop, the flexible wire will tend to change shape from its original configuration to a circular shape. The forces acting on the wire will pull it into a circular form, as this configuration minimizes the potential energy in the magnetic field.

**Hint:** Think about why a circular shape is favored in this context. It is often the most stable configuration under uniform forces.

### Final Answer
The flexible wire loop will change its shape and become circular due to the magnetic forces acting on it when current flows through the wire in the presence of a magnetic field.