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What is the magnetic flux through the loop shown in the figure?
♦ Relevant knowledgeWhen a loop is located in a particular area of magnetic field, so that it is parallel to it, the loop will have the highest possible magnetic flux for the magnetic field ( B). Magnetic flux (Φ) in this scenario is determined by: Φ = B × A where A is the area within the loop.
Magnetic flux through an area of a loop if the magnetic field is perpendicular.
[katex] \Phi_{\mathrm{B}}=B A [/katex]
The loop’s left side is dominated by magnetic flux.
[katex] \begin{aligned} \left(\Phi_{\mathrm{B}}\right)_{\mathrm{left}} &=(2 \mathrm{~T})\left(20 \mathrm{~cm} \frac{1 \mathrm{~m}}{100 \mathrm{~cm}}\right)\left(20 \mathrm{~cm} \frac{1 \mathrm{~m}}{100 \mathrm{~cm}}\right) \\ &=0.08 \mathrm{~T} \cdot \mathrm{m}^{2} \end{aligned} [/katex]
The loop’s right side is dominated by magnetic flux.
[katex] \begin{aligned} \left(\Phi_{\mathrm{B}}\right)_{\mathrm{ight}} &=(1 \mathrm{~T})\left(20 \mathrm{~cm} \frac{1 \mathrm{~m}}{100 \mathrm{~cm}}\right)\left(20 \mathrm{~cm} \frac{1 \mathrm{~m}}{100 \mathrm{~cm}}\right) \\ =& 0.04 \mathrm{~T} \cdot \mathrm{m}^{2} \end{aligned} [/katex]
The net flux through the loop, is
[katex] \begin{aligned} \Phi_{\text {net }} &=\left(\Phi_{\mathrm{B}}\right)_{\text {left }}-\left(\Phi_{\mathrm{B}}\right)_{\text {right }} \\ &=0.08 \mathrm{~T} \cdot \mathrm{m}^{2}-0.04 \mathrm{~T} \cdot \mathrm{m}^{2} \\ &=0.04 \mathrm{~T} \cdot \mathrm{m}^{2} \end{aligned} [/katex]
The net flux is oriented along the left magnetic field of the loop.