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Expert-verified Found in: Page 906 ### Matter & Interactions

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 $0.052T.{m}^{2}$ .

See the step by step solution

## Step 1: Write the given data from the question.

The angle is 300 .

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

## Step 2: Determine the formula

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

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

Consider the simplified form of the equation is:

${\varphi }_{mag}=\int \stackrel{\to }{B}A\mathrm{cos}\theta$

## Step 3: Determine the value of the magnetic field.

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

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

Therefore, the value of the magnetic field is$0.052\text{ T}\cdot {\text{m}}^{2}$ ### Want to see more solutions like these? 