A conducting loop of area 1 m² is placed normal to uniform magnetic field 3 Wb/m². If the magnetic field is uniformly reduced to 1 Wb/m² in a time of 0.5 s, calculate the induced e... A conducting loop of area 1 m² is placed normal to uniform magnetic field 3 Wb/m². If the magnetic field is uniformly reduced to 1 Wb/m² in a time of 0.5 s, calculate the induced emf produced in the loop. Read more

Steps to Solve

1. Identify Given Values

The problem provides the following information:

• Initial magnetic field ($B_1$) = 3 Wb/m²
• Final magnetic field ($B_2$) = 1 Wb/m²
• Area of the loop ($A$) = 1 m²
• Time ($\Delta t$) = 0.5 s

2. Calculate the Change in Magnetic Field

The change in magnetic field ($\Delta B$) can be calculated using: $$ \Delta B = B_2 - B_1 $$ Substituting the values: $$ \Delta B = 1 \text{ Wb/m}^2 - 3 \text{ Wb/m}^2 = -2 \text{ Wb/m}^2 $$

3. Use the Induced EMF Formula

The formula for induced electromotive force (emf) is given by: $$ |\mathcal{E}| = \left| \frac{\Delta B \cdot A}{\Delta t} \right| $$ Substituting the known values: $$ |\mathcal{E}| = \left| \frac{-2 \text{ Wb/m}^2 \cdot 1 \text{ m}^2}{0.5 \text{ s}} \right| $$

4. Calculate the Induced EMF

Perform the calculation: $$ |\mathcal{E}| = \left| \frac{-2}{0.5} \right| $$ This simplifies to: $$ |\mathcal{E}| = |-4| = 4 \text{ V} $$

5. Final Answer

The induced emf produced in the loop is 4 V.