If the instantaneous magnetic flux and induced emf produced in a coil is `phi` and `E` respectively, then a according to Faraday's law of electromagetic induction

Options

A. E must be zero if `phi=0`
B. `E!=0 if phi=0`
C. `E!=0` but `phi` may or may not be zero
D. E=0 then `phi` must be zero

Explanation

To solve the problem based on Faraday's law of electromagnetic induction, we need to analyze the statements given in the options (A, B, C, D) regarding the relationship between magnetic flux (Φ) and induced electromotive force (E).

### Step-by-Step Solution:

1. **Understanding Faraday's Law**:
Faraday's law states that the induced electromotive force (E) in any closed circuit is equal to the negative rate of change of magnetic flux (Φ) through the circuit. Mathematically, it can be expressed as:
\[ E = -\frac{d\Phi}{dt} \]
This means that if the magnetic flux is changing over time, an induced emf will be generated.

**Hint**: Remember that induced emf is related to the rate of change of magnetic flux.

2. **Analyzing Option A**:
The first option states that if Φ = 0, then E must also be 0. This is not necessarily true. The induced emf depends on the rate of change of flux, not just the value of flux itself. If the flux is zero but changing (for example, increasing from a negative value), the induced emf can be non-zero.

**Hint**: Consider the situation where the flux is zero but changing over time.

3. **Analyzing Option B**:
The second option suggests that if Φ = 0, then the electric field (E) will be non-zero. This statement is also misleading. The electric field induced in the coil depends on the rate of change of flux. If the flux is zero but changing, the electric field can be non-zero. However, if the flux is constant (including being zero), the electric field will be zero.

**Hint**: Think about the relationship between electric field and the change in magnetic flux.

4. **Analyzing Option C**:
The third option states that the electric field is non-zero, and Φ may or may not be zero. This statement is correct. The electric field can be induced by a changing magnetic flux, regardless of whether the instantaneous value of flux is zero or not.

**Hint**: Remember that the electric field is related to the rate of change of flux, not its absolute value.

5. **Analyzing Option D**:
The fourth option claims that if the electric field is zero, then the flux must also be zero. This is incorrect. The electric field being zero indicates that there is no change in flux (i.e., the flux is constant), but it does not necessarily mean that the flux itself is zero. It could be a constant non-zero value.

**Hint**: Consider the implications of a constant magnetic flux on the induced electric field.

### Conclusion:
Based on the analysis of the options, Option C is the correct statement. The electric field can be non-zero while the magnetic flux may or may not be zero, as long as there is a change in the magnetic flux.

**Final Answer**: The correct option is C.