If the flux associated with a coil varies at the rate of 1 Wb/min, the induced emf is

Options

A. 1 V
B. 1/60 V
C. 60 V
D. zero

Explanation

To solve the problem of finding the induced electromotive force (emf) when the magnetic flux associated with a coil varies at a rate of 1 Wb/min, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Induced EMF**:
The induced emf (ε) in a coil is given by Faraday's law of electromagnetic induction:
\[ \text{EMF} = -\frac{d\Phi}{dt} \]
where \(d\Phi\) is the change in magnetic flux and \(dt\) is the change in time.

2. **Identify the Given Values**:
From the problem, we know:
- The rate of change of magnetic flux \(d\Phi\) is 1 Weber (Wb) per minute.
- We need to convert this rate into seconds since the standard unit of time in physics is seconds.

3. **Convert Time from Minutes to Seconds**:
Since 1 minute equals 60 seconds, we can express the rate of change of flux in terms of seconds:
\[ d\Phi = 1 \text{ Wb}, \quad dt = 1 \text{ min} = 60 \text{ seconds} \]

4. **Calculate the Rate of Change of Flux**:
Now, we can find \(\frac{d\Phi}{dt}\):
\[ \frac{d\Phi}{dt} = \frac{1 \text{ Wb}}{60 \text{ s}} = \frac{1}{60} \text{ Wb/s} \]

5. **Substitute into the EMF Formula**:
Now, substituting this value into the formula for induced emf:
\[ \text{EMF} = -\frac{d\Phi}{dt} = -\frac{1}{60} \text{ V} \]
Since we are interested in the magnitude of the induced emf, we can ignore the negative sign:
\[ \text{EMF} = \frac{1}{60} \text{ V} \]

6. **Final Answer**:
Therefore, the induced emf is:
\[ \text{EMF} = \frac{1}{60} \text{ V} \approx 0.01667 \text{ V} \]