Question

A circular area with a radius of 6.00 cm lies in the xy-plane. 

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Part A What is the magnitude of the magnetic flux through this circle due to a uniform magnetic field with a magnitude of 0.220 T in the + z-direction? 

Part B What is the magnitude of the magnetic flux through this circle due to the same magnetic field (with a magnitude of 0.220 T ), now at an angle of 53.8 from the + z-direction? 

Part C What is the magnitude of the magnetic flux through this circle due to the same magnetic field (with a magntiude of 0.220 T ), now in the + y -direction? 

Answer 1

\(A\) )

The magnetic flux through the circle is

$$ \begin{aligned} \phi_{\mathrm{B}} &=B A \cos 0^{\circ} \\ &=(0.220 \mathrm{~T})\left(\pi\left(6.00 \times 10^{-2} \mathrm{~m}\right)^{2}\right) \\ &=2.488 \times 10^{-3} \mathrm{~T} \cdot \mathrm{m}^{2}=2.49 \times 10^{-3} \mathrm{~T} \cdot \mathrm{m}^{2} \end{aligned} $$

B) The magnetic flux through the circle is

$$ \begin{aligned} \phi_{\mathrm{B}} &=B A \cos 53.8^{\circ} \\ &=(0.220 \mathrm{~T})\left(\pi\left(6.00 \times 10^{-2} \mathrm{~m}\right)^{2}\right) \cos 53.8^{\circ} \\ &=1.47 \times 10^{-3} \mathrm{~T} \cdot \mathrm{m}^{2} \end{aligned} $$

C)

The magnetic flux through the circle is

$$ \begin{aligned} \phi_{\mathrm{B}} &=B A \cos 90^{\circ} \\ &=0 \end{aligned} $$