Find the magnetic flux through a 5.0 -cm-diameter circular loop oriented with the loop normal at \(30^{\circ}\) to a uniform 80 -mT magnetic field.

Short Answer

Expert verified
The magnetic flux through the circular loop in the given magnetic field at the given orientation is calculated in Step 3 of the solution. The detailed computation would depend on the exact calculated area from Step 1 and could be completed as described in Steps 2 and 3.

Step by step solution

01

Calculation of Loop Area

Given that the diameter of the circular loop is 5.0 cm, use this to calculate the radius (r), i.e., \(r = \frac{Diameter}{2} = \frac{5.0cm}{2} = 2.5 cm = 0.025 m\). Then, apply the formula of the area of a circle \(A = \pi r^2\) to find the area.
02

Input Known Values into Flux Equation

Plug all known values into the magnetic flux equation. In this problem, the magnetic field (B) is 80 mT (0.08 T), the area (A) was calculated in the previous step, and the angle \(x = 30^{\circ}\). So, we get \(\Phi_B = 0.08 T \cdot A \cdot cos(30^{\circ})\).
03

Computation of Magnetic Flux

After substituting the computed area and given magnetic field and angle into the equation, calculate the resulting magnetic flux. Remember that angle should be used in radians when calculating cosine in most calculators. 30 degrees equals \(\frac{\pi}{6}\) radians.

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