Flux density from flux and area: In a magnetic field, a flux of 600 µWb passes through an area of 0.1 m^2. Calculate the flux density B.

Introduction / Context:Flux density B quantifies how much magnetic flux passes per unit area and is a central concept in electromagnetics, affecting induced voltages and magnetic forces. It connects the physical flux to field intensity via the area considered.

Given Data / Assumptions:

• Total magnetic flux, phi = 600 µWb = 600 * 10^-6 Wb.
• Area, A = 0.1 m^2.
• Uniform flux distribution is assumed over the area for a straightforward calculation.

Concept / Approach:

By definition, B = phi / A. Convert all units to SI before dividing. 1 tesla (T) equals 1 Wb/m^2. You can also express the result in microtesla (µT) for convenience, where 1 T = 10^6 µT.

Step-by-Step Solution:

Verification / Alternative check:

A quick order-of-magnitude check: micro–weber over a tenth of a square meter should yield milli–tesla or thousands of microtesla, consistent with 6,000 µT.

Why Other Options Are Wrong:

600 µT is a factor of 10 too small; 6 T and 600 T are far too large given the small flux and moderate area; 60 µT is two orders too small.

Common Pitfalls:

Missing the micro (10^-6) prefix or forgetting to divide by area correctly. Always standardize units first to avoid errors.

Final Answer:

6,000 µT