Magnetic Induced Emf is equal to ?

Options

A. `dphi //dt`
B. `dm // dt`
C. `dphi + dt`
D. `dl ^(**) dt`

Explanation

To determine the magnetic induced EMF, we can follow these steps:

### Step 1: Understand the Concept of Magnetic Flux
Magnetic flux (Φ) is defined as the product of the magnetic field (B) and the area (A) through which the field lines pass, taking into account the angle (θ) between the magnetic field and the normal to the surface:
\[ \Phi = B \cdot A \cdot \cos(\theta) \]

### Step 2: Define Induced EMF
According to Faraday's law of electromagnetic induction, the induced electromotive force (EMF) in a closed loop is equal to the negative rate of change of magnetic flux through the loop:
\[ \text{Induced EMF} = -\frac{d\Phi}{dt} \]

### Step 3: Apply the Concept
The induced EMF can be expressed as:
\[ \text{Induced EMF} = -\frac{d(B \cdot A \cdot \cos(\theta))}{dt} \]
However, for the purpose of this question, we are primarily concerned with the rate of change of magnetic flux itself, which simplifies to:
\[ \text{Induced EMF} = \frac{d\Phi}{dt} \]

### Step 4: Identify the Correct Option
From the options provided, the correct expression for magnetic induced EMF is:
\[ \text{Induced EMF} = \frac{d\Phi}{dt} \]
This corresponds to the first option given in the question.

### Conclusion
Thus, the magnetic induced EMF is equal to the rate of change of magnetic flux with respect to time:
\[ \text{Induced EMF} = \frac{d\Phi}{dt} \]

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