Question

Rearrange the equation to solve for the permeability of free space (μ0). Remember that the slope is the ratio of magnetic field to current or μ0 = 2R N B I . Hint: Substitute your value of slope into the equation in place of B / I. μ0 = T · m/A

Answer 1

Complete Question

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Compare the percent error between your value and the accepted value of 1.26 times 10-6 T · m/A. (Use the accepted value given to three significant figures in your calculation.). 100% % error = %

Answer:

The permeability of free space is $\mu_0 = 1.32*10^{-6} \ Tm/A$

The percentage error is  % error = 5.25%

Explanation:

From the question we are told that

            The slope is  $s= 3.9\ G/A$ , and

Generally  $1 \ gauss = 10^{-4 } tesla$

               So  $s = 3.9 *10^ {-4} T /A$

From the relation given in the question

                        $\mu_0 = \frac{2R}{N} [\frac{B}{I} ]$

 Where R is the radius of the coil  $=\frac{Diameter \ of \ coil }{2} = 0.017m$

             N is the number of loops of the coil = 10

Now from the question we are told that

                  $s = \frac{B}{I}$

substituting into the equation above

               $\mu_0 = \frac{2R }{N} s$

Substituting values

              $\mu_0= \frac{2 * 0.017}{10 } * 3.9*10^{-4}$

                   $= 1.326 *10^ {-6} \ Tm/A$

Generally the % error is mathematically represented as

                    %$error = \frac{Measured \ value - accepted \ value}{accepted \ value } *100$

Given that the accepted value is $\mu_o_ {acc} = 1.26 *10 ^{-6} \ T \cdot m /A$

      Hence substituting values

                      %$error = \frac{(1.326-1.26)*10^{-6}}{1.26 *10 ^ {-6}} *100$

                                  $= 5.24$