Curves in the graph shown in Fig. give, as function of radius distance r, the magnitude B of the magnetic field inside and outside four long wire a,b,c and d, carrying currents that are uniformly distributed across the cross sections of the wires. Overlapping portions of the plots are indicated by double labels.
Which wire has the greatest radius?

A. a
B. b
C. c
D. d

Options

A. `a`
B. `b`
C. ` c`
D. `d`

Explanation

To solve the question of which wire has the greatest radius based on the provided graph of magnetic field strength as a function of radius, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Magnetic Field Behavior**:
The magnetic field \( B \) inside a long straight wire carrying a current is given by the formula:
\[ B = \frac{\mu_0 I r}{2 \pi R^2} \]
where \( \mu_0 \) is the permeability of free space, \( I \) is the current, \( r \) is the distance from the center of the wire, and \( R \) is the radius of the wire.

2. **Analyze the Graph**:
The graph shows the magnetic field \( B \) as a function of the radius \( r \) for four wires (A, B, C, and D). The curves represent the magnetic field inside and outside each wire.

3. **Identify the Regions of the Graph**:
- Inside the wire, the magnetic field increases linearly with \( r \) until it reaches the wire's radius \( R \).
- Outside the wire, the magnetic field decreases with \( 1/r \).

4. **Look for Maximum Radius**:
To determine which wire has the greatest radius, we need to identify the point where each wire's curve transitions from the linear increase (inside the wire) to the decrease (outside the wire). This transition point indicates the radius of the wire.

5. **Compare the Transition Points**:
By examining the graph:
- Identify the point where each wire's curve ends (the maximum radius).
- Compare these points for wires A, B, C, and D.

6. **Conclusion**:
From the analysis of the graph, it is observed that wire C has the highest transition point, indicating that it has the greatest radius compared to wires A, B, and D.

### Final Answer:
The wire with the greatest radius is **C**.

---