If J-²-cosā, +sin 0 A/m², find the current (I) passing through (a) A hemispherical shell of radius 15 cm, 0<0<.0< p <2n (b) A spherical shell of radius 5 cm

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**Problem Statement:**

If \(\vec{J} = \frac{3}{r} \cos \theta \, \vec{a}_r + \frac{4}{r} \sin \theta \, \vec{a}_\theta \, \text{A/m}^2\), find the current \(I\) passing through:

(a) A hemispherical shell of radius 15 cm, \(0 < \theta < \frac{\pi}{2}, 0 < \phi < 2\pi\)

(b) A spherical shell of radius 5 cm

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**Explanation:**

- The problem involves calculating the current \(I\) from a given current density vector \(\vec{J}\).
- There are two scenarios provided to find the current passing through different geometrical shapes, specifically a hemispherical shell and a spherical shell.
- The expressions involve spherical coordinates with \(\theta\) and \(\phi\) indicating the angular parameters.

No graphs or diagrams are associated with this content.
Transcribed Image Text:Certainly! Here is the transcribed text for educational purposes: --- **Problem Statement:** If \(\vec{J} = \frac{3}{r} \cos \theta \, \vec{a}_r + \frac{4}{r} \sin \theta \, \vec{a}_\theta \, \text{A/m}^2\), find the current \(I\) passing through: (a) A hemispherical shell of radius 15 cm, \(0 < \theta < \frac{\pi}{2}, 0 < \phi < 2\pi\) (b) A spherical shell of radius 5 cm --- **Explanation:** - The problem involves calculating the current \(I\) from a given current density vector \(\vec{J}\). - There are two scenarios provided to find the current passing through different geometrical shapes, specifically a hemispherical shell and a spherical shell. - The expressions involve spherical coordinates with \(\theta\) and \(\phi\) indicating the angular parameters. No graphs or diagrams are associated with this content.
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