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The magnetic field perpendicular to the plane of a loop of area `0.1m^(2)` is 0.2 T. Calculate the magnetic flux through the loop (in weber)

A

0.01

B

0.02

C

0.03

D

0.04

Text Solution

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The correct Answer is:
To calculate the magnetic flux through the loop, we can follow these steps: ### Step 1: Understand the Formula for Magnetic Flux The magnetic flux (Φ) through a surface is given by the formula: \[ Φ = B \cdot A \cdot \cos(θ) \] where: - \( Φ \) is the magnetic flux in webers (Wb), - \( B \) is the magnetic field strength in teslas (T), - \( A \) is the area of the surface in square meters (m²), - \( θ \) is the angle between the magnetic field and the normal (perpendicular) to the surface. ### Step 2: Identify the Given Values From the problem, we have: - Area of the loop, \( A = 0.1 \, m² \) - Magnetic field strength, \( B = 0.2 \, T \) - Since the magnetic field is perpendicular to the plane of the loop, the angle \( θ = 0° \). ### Step 3: Calculate the Cosine of the Angle Since \( θ = 0° \): \[ \cos(0°) = 1 \] ### Step 4: Substitute the Values into the Formula Now we can substitute the values into the magnetic flux formula: \[ Φ = B \cdot A \cdot \cos(θ) = 0.2 \, T \cdot 0.1 \, m² \cdot 1 \] ### Step 5: Perform the Calculation Calculating the above expression: \[ Φ = 0.2 \cdot 0.1 \cdot 1 = 0.02 \, Wb \] ### Conclusion The magnetic flux through the loop is: \[ Φ = 0.02 \, Wb \] ---
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