Question

If ε and ∆t are the induced EMF and time respectively, then the change in magnetic flux is given by

• A. \(\frac{ ε}{\Delta t}\)
• B. \(ε∆t\)
• C. \(\sqrt{\frac{ ε}{\Delta t}}\)
• D. \(\sqrt{ε∆t}\)

Answer 1

The Correct Option is B

To find the change in magnetic flux, we need to use Faraday's Law of Electromagnetic Induction, which relates the induced electromotive force (EMF) \(ε\) in a closed circuit to the rate of change of magnetic flux through the circuit. The formula is given by:

\[\epsilon = -\frac{\Delta \Phi}{\Delta t}\]

where:

• \( \epsilon \) is the induced EMF
• \( \Delta \Phi \) is the change in magnetic flux
• \( \Delta t \) is the time interval

Rearranging the formula to solve for the change in magnetic flux \( \Delta \Phi \), we have:

\[\Delta \Phi = -\epsilon \Delta t\]

Since we are focusing on the magnitude of the change, we can express it as:

\[\Delta \Phi = \epsilon \Delta t\]

Therefore, the change in magnetic flux is given by the product of the induced EMF and the time period. 

Answer 2

According to Faraday’s Law of Electromagnetic Induction, the magnitude of induced EMF is given by:

\[ \varepsilon = \frac{\Delta \Phi}{\Delta t} \]

Where:

• \( \varepsilon \) is the induced EMF
• \( \Delta \Phi \) is the change in magnetic flux
• \( \Delta t \) is the time over which the change occurs

Rearranging the formula to find \( \Delta \Phi \):

\[ \Delta \Phi = \varepsilon \cdot \Delta t \]

Correct Answer: \( \varepsilon \Delta t \)