Finding Centre of Hemisphere - Radius a

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In summary, the conversation is about finding the value of z that corresponds to the center of a hemisphere with radius a and the z-axis as its axis. The person initially suggests using z = a/2 but is unsure if it's the correct value. They then clarify that they are not looking for the center of mass and are discussing the top half of a solid sphere. The main question is how to find the electric field at the center of the hemisphere, with the person asking for help in determining the correct z value to use for their expression.
  • #1
latentcorpse
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imagine a hemisphere of radius a with the circle lying in the x-y plane and so the axis of the hemisphere is the z axis. if z=0 is at the centre of our circle, what value of z corresponds to the centre of the hemisphere?

i used z=a/2 but have a sneaky feeling its' meant to be [itex]\frac{a}{\sqrt{2}}[/itex]

can anyone help?
 
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  • #2
Do you want the CENTER OF MASS?

Are you looking at the top half of a solid sphere centered at the origin with radius a?
 
  • #3
i don't want the centre of mass. yes your talking about the right shape.

basically i have an expression for the electric field on the z axis as the hemispherical surface is charged and it asks me to find the value of the electric field at the centre of the hemisphere - what z value should i use?
 

FAQ: Finding Centre of Hemisphere - Radius a

1. What is the formula for finding the center of a hemisphere with radius a?

The formula for finding the center of a hemisphere with radius a is (0,0,a/2). This means that the center is located at the origin, with a distance of a/2 from the base of the hemisphere.

2. How is the center of a hemisphere related to its radius a?

The center of a hemisphere is directly related to its radius a. As mentioned before, the center is located at the origin with a distance of a/2 from the base. This means that the center is always half of the radius value.

3. Can the center of a hemisphere be located at any other point?

No, the center of a hemisphere can only be located at the origin. This is because a hemisphere is a symmetrical shape and the center point must align with the axis of symmetry.

4. How is finding the center of a hemisphere useful in real life applications?

Finding the center of a hemisphere is useful in various fields such as engineering, architecture, and physics. It is used to determine the point of balance and stability for structures and objects, as well as to calculate the volume and surface area of a hemisphere.

5. Is there a difference between the center of a hemisphere and the center of mass?

Yes, there is a difference between the center of a hemisphere and the center of mass. The center of a hemisphere refers to a specific point on the shape, while the center of mass is the point at which the mass of an object is evenly distributed. However, for a symmetrical hemisphere, the center of mass and the center of the shape will coincide.

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