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en/9.3.22.md
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| + | ### Statement | ||
| + | |||
| + | $9.3.22.$ [Insert the problem statement] | ||
| + | |||
| + | ### Solution | ||
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| + | a) As in the previous problem, we will use the property of the vector product and the formula for the field inside a cylindrical wire. Consider a point at distances $r_1$ and $r_2$ from the centers of the cylinders: | ||
| + | $$\hat{B} = \frac{\mu_0 [\hat{r}_1 \times \hat{j}]}{2} - \frac{\mu_0 [\hat{r}_2 \times \hat{j}]}{2} = \frac{\mu_0 [\hat{a} \times \hat{j}]}{2}$$ | ||
| + | $$B = \frac{\mu_0 a j}{2}$$ | ||
| + | b) The detailed solution to this point repeats in all its main points the solution to problem 6.2.14, which I recommend you read. However, it should be mentioned that here it is more convenient to express the answer in terms of a sine, since the induction lines inside are perpendicular to the vector $\hat{a}$. | ||
| + | $$i = j a sin \varphi$$ | ||
| + | $$j = \frac{2B_0}{\mu_0 a}$$ | ||
| + | $$i = \frac{2B_0}{\mu_0}sin\varphi$$ | ||
| + | $$i_{max} = \frac{2B_0}{\mu_0}$$ | ||
| + | |||
| + | #### Answer | ||
| + | |||
| + | [Insert a concise answer or boxed result] | ||
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| ### Statement | |||
| $9.3.22.$ [Insert the problem statement] | |||
| ### Solution | |||
| a) As in the previous problem, we will use the property of the vector product and the formula for the field inside a cylindrical wire. Consider a point at distances $r_1$ and $r_2$ from the centers of the cylinders: | |||
| $$\hat{B} = \frac{\mu_0 [\hat{r}_1 \times \hat{j}]}{2} - \frac{\mu_0 [\hat{r}_2 \times \hat{j}]}{2} = \frac{\mu_0 [\hat{a} \times \hat{j}]}{2}$$ | |||
| $$B = \frac{\mu_0 a j}{2}$$ | |||
| b) The detailed solution to this point repeats in all its main points the solution to problem 6.2.14, which I recommend you read. However, it should be mentioned that here it is more convenient to express the answer in terms of a sine, since the induction lines inside are perpendicular to the vector $\hat{a}$. | |||
| $$i = j a sin \varphi$$ | |||
| $$j = \frac{2B_0}{\mu_0 a}$$ | |||
| $$i = \frac{2B_0}{\mu_0}sin\varphi$$ | |||
| $$i_{max} = \frac{2B_0}{\mu_0}$$ | |||
| #### Answer | |||
| [Insert a concise answer or boxed result] | |||