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A circular loop with a radius of 9.792 cm is positioned in various orientations in a uniform magnetic field of 1.194 T. Find the magnetic flux if the normal to the plane of the loop is parallel to the field.

User Pattie
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The magnetic flux Φ of a field B on a loop with area A and normal vector n is:


\Phi=BA\cos\theta

There θ is the angle between the normal vector n and the field B.

If the normal to the plane of the loop is parallel to the field, then θ=0º. In that case, the magnetic flux is simply the product of the field and the area of the loop, since cos(θ)=0:


\begin{gathered} \theta=0 \\ \Rightarrow \\ \Phi=BA \end{gathered}

The area of a circle with radius r is:


A=\pi r^2

Replace the expression for the area in terms of r and substitute B=1.194T and r=9.792*10^(-2)m to find the magnetic flux:


\begin{gathered} \Phi=BA \\ \\ =B\cdot\pi r^2 \\ \\ =1.194T\cdot\pi(9.792*10^(-2)m)^2 \\ \\ =0.0359664...Tm^2 \\ \\ \approx0.03597Wb \end{gathered}

Therefore, the magnetic flux if the normal is parallel to the field, is 0.03597 weber.

User DougC
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