Practice - Faraday’s Law

Section 28.7 Practice - Faraday’s Law

ARC*S 28.7.1. Magnetic Flux.

What is the magnetic flux through an equilateral triangle with side \(60 \mathrm{~cm},\) long, whose plane makes a 60 degree angle with a uniform magnetic field of \(0.33 \mathrm{~T}\text{?}\)

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Explanation 28.7.2. The Moving Wire Loop.

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The square wire loop below is located below a long straight wire carrying current \(I_w\text{.}\) Each side of the circuit has length \(l\text{.}\)

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Figure 28.7.1. A square wire loop moving upward toward a wire.
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Make a magnetic induction table for each of the following cases:

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The loop is moving upward with constant speed \(v\text{.}\) Choose an area vector into the page.
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Repeat case A, but choose the area vector to be in the opposite direction.
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Repeat case A, but now the loop is moving downward with constant speed \(v\text{.}\)
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Repeat case A, but now the loop is moving to the left with constant speed \(v\text{.}\)
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Repeat case A, but now the loop is stationary and the long straight wire is moving upward with constant speed \(v\text{.}\)
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Table 28.7.2. Blank Magnetic Induction Table

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Quantity	Case A	Case B	Case C	Case D	Case E
\(\vec{A}\)
\(\vec{B}\)
\(\Phi_B\)
\(\frac{d\Phi_B}{dt}\)
\(V_{ind}\)
\(I_{ind}\)
\(\vec{\mu}_{ind}\)

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Subsubsection ARC*S Practice

ARC*S 28.7.3. Square Loop in a Magnetic Field.

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A square loop of wire with side length 6 cm and resistance 0.4 \(\Omega\) is in a uniform magnetic field \(B = -0.008t^2\) (in Tesla) that points in the \(z\)-direction (through the loop). Determine the current induced in the loop as a function of time (both magnitude and direction).

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Subsubsection Numerical Practice

Calculation 28.7.4. Induced Current.

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A single conducting loop of wire has an area of \(7.40 \times 10^{-2} \ \mathrm{m}^2\) and a resistance of 110 \(\Omega\text{.}\) Perpendicular to the plane of the loop is a magnetic field of strength 0.280 T. At what rate (in T/s) must this field change if the induced current in the loop is to be 0.32 A?

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Answer.

476 T/s

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Figure 28.7.3. Circular conductive loop in a uniform magnetic field.
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Calculation 28.7.5. Conductive Loop in a Magnetic Field.

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A conductive metal loop is at rest within a uniform magnetic field, as shown above. If the magnetic field strength is then decreased, in which direction does induced current flow in the loop?

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Answer.

There is no current.

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Figure 28.7.4. Circular conductive loop falling away from a current carrying wire.
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Calculation 28.7.6. Falling Loop.

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The figure shows a circular conductive loop falling away from a long wire that is carrying current to the right, as shown above. What is the direction of the induced current in the loop?

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Answer.

Clockwise.

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