shows a conducting loop being pulled out of a magnetic field with a speed v. Which of lthe four plots shown in may represent the power delivered by the pulling agent as a function of the speed v ?
a
b
c
d

Options

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

Explanation

To solve the problem of determining which plot represents the power delivered by the pulling agent as a function of speed \( v \) for a conducting loop being pulled out of a magnetic field, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Induced EMF**:
The induced electromotive force (EMF) in the loop can be expressed using Faraday's law of electromagnetic induction. For a loop being pulled out of a magnetic field with a velocity \( v \), the induced EMF (\( \mathcal{E} \)) is given by:
\[ \mathcal{E} = B \cdot L \cdot v \]
where \( B \) is the magnetic field strength, \( L \) is the length of the loop, and \( v \) is the velocity.

**Hint**: Remember that the induced EMF is directly proportional to the velocity of the loop.

2. **Calculate the Power**:
The power (\( P \)) delivered by the pulling agent can be calculated using the formula:
\[ P = \frac{\mathcal{E}^2}{R} \]
where \( R \) is the resistance of the loop. Substituting the expression for EMF, we get:
\[ P = \frac{(B \cdot L \cdot v)^2}{R} \]

3. **Simplify the Power Expression**:
Simplifying the expression for power, we have:
\[ P = \frac{B^2 \cdot L^2 \cdot v^2}{R} \]
This shows that power \( P \) is proportional to the square of the velocity:
\[ P \propto v^2 \]

**Hint**: Identify the relationship between power and velocity; it is quadratic.

4. **Determine the Graph Shape**:
Since \( P \) is proportional to \( v^2 \), the graph of power versus velocity will be a parabola opening upwards. This means as the velocity increases, the power increases with the square of the velocity.

5. **Select the Correct Plot**:
Among the given options (a, b, c, d), we need to identify which one represents a parabolic relationship. The correct plot will show a curve that starts at the origin and rises steeply as \( v \) increases.

**Hint**: Look for a graph that resembles a quadratic function, typically shaped like a "U".

### Conclusion:
Based on the analysis, the correct option that represents the power delivered by the pulling agent as a function of speed \( v \) is **option B**, which shows a parabolic relationship.