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Q3CP

Expert-verifiedFound in: Page 906

Book edition
4th edition

Author(s)
Ruth W. Chabay, Bruce A. Sherwood

Pages
1135 pages

ISBN
9781118875865

**:A uniform magnetic field of 3 T points ${{\mathbf{30}}}^{{\mathbf{0}}}$ away from the perpendicular to the plane of a rectangular loop of wire 0.1 m by 0.2 m (Figure 22.14). What is the magnetic flux on this loop?**

The value of the magnetic field is $0.052T.{m}^{2}$ .

The angle is 30^{0} .

The dimension of the rectangular wire is 0.1 m by 0.2 m.

**Consider the formula for the magnetic flux in the loop as:**

${\varphi}_{mag}=\int \overrightarrow{B}\cdot dA$

**Consider the simplified form of the equation is:**

**${\varphi}_{mag}=\int \overrightarrow{B}A\mathrm{cos}\theta $**

Substitute the values in the formula for the magnetic field and solve as:

$\begin{array}{l}{\varphi}_{mag}=\left(3\text{\hspace{0.33em}T}\right)\left(0.01\text{\hspace{0.33em}m}\times \text{0.2\hspace{0.33em}m}\right)\mathrm{cos}30\xb0\\ {\varphi}_{mag}=\left(3\text{\hspace{0.33em}T}\right)\left(0.02{\text{\hspace{0.33em}m}}^{2}\right)\mathrm{cos}30\xb0\\ {\varphi}_{mag}=0.052\text{\hspace{0.33em}T}\cdot {\text{m}}^{2}\end{array}$

Therefore, the value of the magnetic field is$0.052\text{\hspace{0.33em}T}\cdot {\text{m}}^{2}$

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