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Lesson #29: Biot-Savart Law Name: Study section 5.1-5.2, especially examples 5.5 and 5.6, then answer the following questions. Express your answers in terms of the given parameters and fundamental constants. A phonograph record (radius R) carries a uniform charge density ?. It rotates at angular velocity ? in a direction that is ccw for an observer looking down on the record from point P. 1. The spinning disk of charge constitutes a surface current; write down an expression for the surface current density in terms of given parameters: K = 2. Sketch and label the vector \(\vec{K}\), the surface current density, for two different points on the disk. 3. The spinning disk will create a magnetic field; sketch and label a few field lines on the figure above. 4. Does your sketch show that \(\nabla \cdot \vec{B} = 0\)? Explain how your sketch satisfies this equation. 5. Write down an expression for the magnetic field, B, in terms of K and \(\vec{r}\), the separation vector: B = 6. Sketch the vectors \(\vec{r}\), \(\vec{r'}\) and \(\vec{r}\) on the figure to the right. 7. Plug in expressions for K and \(\vec{r}\) to solve for the magnetic field at Point P. Set up and completely specify the integral that needs to be solved; you don't need to evaluate it. B =

          Lesson #29: Biot-Savart Law
Name:
Study section 5.1-5.2, especially examples 5.5 and 5.6, then answer the following questions. Express your answers in
terms of the given parameters and fundamental constants.
A phonograph record (radius R) carries a uniform charge density ?. It
rotates at angular velocity ? in a direction that is ccw for an observer
looking down on the record from point P.
1. The spinning disk of charge constitutes a surface current; write down an
expression for the surface current density in terms of given parameters:
K =
2. Sketch and label the vector \(\vec{K}\), the surface current density, for two
different points on the disk.
3. The spinning disk will create a magnetic field; sketch and label a few field lines on the figure above.
4. Does your sketch show that \(\nabla \cdot \vec{B} = 0\)? Explain how your sketch satisfies this equation.
5. Write down an expression for the magnetic field, B, in terms of K and \(\vec{r}\), the separation vector:
B =
6. Sketch the vectors \(\vec{r}\), \(\vec{r'}\) and \(\vec{r}\) on the figure to the right.
7. Plug in expressions for K and \(\vec{r}\) to solve for the magnetic field at Point P. Set up and completely
specify the integral that needs to be solved; you don't need to evaluate it.
B =

Lesson #29: Biot-Savart Law
Name:
Study section 5.1-5.2, especially examples 5.5 and 5.6, then answer the following questions. Express your answers in
terms of the given parameters and fundamental constants.
A phonograph record (radius R) carries a uniform charge density ?. It
rotates at angular velocity ? in a direction that is ccw for an observer
looking down on the record from point P.
1. The spinning disk of charge constitutes a surface current; write down an
expression for the surface current density in terms of given parameters:
K =
2. Sketch and label the vector K⃗, the surface current density, for two
different points on the disk.
3. The spinning disk will create a magnetic field; sketch and label a few field lines on the figure above.
4. Does your sketch show that ∇·B⃗ = 0? Explain how your sketch satisfies this equation.
5. Write down an expression for the magnetic field, B, in terms of K and r⃗, the separation vector:
B =
6. Sketch the vectors r⃗, r⃗'⃗ and r⃗ on the figure to the right.
7. Plug in expressions for K and r⃗ to solve for the magnetic field at Point P. Set up and completely
specify the integral that needs to be solved; you don't need to evaluate it.
B =

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