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

**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?

Revelant knowledge

Magnetic Flux: The term “magnetic flux” can be described as a measurement of the amount of lines in the magnetic field which pass through an area. The magnetic flux will be influenced by the intensity of magnetic fields which is the density of the lines of magnetic field as well as the size of the area and also the angle of the area in relation to that field. This means that if a area’s plane is in line with that field then no field lines will be able to pass through the area. Thus, the bigger magnetic field, greater the flux and the bigger the area, and the greater the flux. Likewise, the more perpendicular the plan of the area to the magnetic field the higher the flux.

Part A:The magnetic flux that runs through the circle is:[katex] \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} [/katex]

Part B:The magnetic flux that runs through the circle is:[katex] \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} [/katex]

Part C:The magnetic flux that runs through the circle is:[katex] \begin{aligned} \phi_{\mathrm{B}} &=B A \cos 90^{\circ} \\ &=0 \end{aligned} [/katex]