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Using a symmetry argument, explain why, for points on the positive z-axis, the gravitational field points towards the centre of the disk, i.e. parallel to the z-axis. Starting from the gravitational potential, and using the answer to 4., derive an expression for the gravitational field a for points on the positive z-axis. What does this become in the limit R → 0? (Brain teaser) Show that the potential o “becomes infinite" in that same limit. How can you get round this problem, to find the gravitational field from the potential even in the limit R→ 0?

Using a symmetry argument, explain why, for points on the positive z-axis, the gravitational field points towards the centre of the disk, i.e. parallel to the z-axis. Starting from the gravitational potential, and using the answer to 4., derive an expression for the gravitational field a for points on the positive z-axis. What does this become in the limit R → 0? (Brain teaser) Show that the potential o “becomes infinite" in that same limit. How can you get round this problem, to find the gravitational field from the potential even in the limit R→ 0?

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Consider a thin disc of radius R and consisting of a material with constant mass density (per unit of area) g. Use cylindrical coordinates, with the z-axis perpendicular to the plane of the disc, and the origin at the disc's centre. We are going to calculate the gravitational potential, and the gravitational field, in points on the z-axis only. the gravitational potential p(2) set up by that disc is given by dr'; ()² + z² sp(2) = 27Gg
Transcribed Image Text:Consider a thin disc of radius R and consisting of a material with constant mass density (per unit of area) g. Use cylindrical coordinates, with the z-axis perpendicular to the plane of the disc, and the origin at the disc's centre. We are going to calculate the gravitational potential, and the gravitational field, in points on the z-axis only. the gravitational potential p(2) set up by that disc is given by dr'; ()² + z² sp(2) = 27Gg
Using a symmetry argument, explain why, for points on the positive z-axis, the gravitational field points towards the centre of the disk, i.e. parallel to the z-axis. Starting from the gravitational potential, and using the answer to 4., derive an expression for the gravitational field a for points on the positive z-axis. What does this become in the limit R → ? (Brain teaser) Show that the potential o “becomes infinite" in that same limit. How can you get round this problem, to find the gravitational field from the potential even in the limit R→ 0?
Transcribed Image Text:Using a symmetry argument, explain why, for points on the positive z-axis, the gravitational field points towards the centre of the disk, i.e. parallel to the z-axis. Starting from the gravitational potential, and using the answer to 4., derive an expression for the gravitational field a for points on the positive z-axis. What does this become in the limit R → ? (Brain teaser) Show that the potential o “becomes infinite" in that same limit. How can you get round this problem, to find the gravitational field from the potential even in the limit R→ 0?
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