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typo "electric fields" $\rightarrow$ "gravitational fields"
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Chris
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enter image description here

In this problem, I understand that the modulus of the electricgravitational fields must be equal;equal, however I'm not quite able to understand the calculation of potential due to each portion.

I tried calculating the potential by considering differential rings and integrating over the angle subtended at the given point... but it gets very messy and is clearly out of my scope. Is there an analytical way to approach this problem?

enter image description here

In this problem, I understand that the modulus of the electric fields must be equal; however I'm not quite able to understand the calculation of potential due to each portion.

I tried calculating the potential by considering differential rings and integrating over the angle subtended at the given point.. but it gets very messy and is clearly out of my scope. Is there an analytical way to approach this problem?

enter image description here

In this problem, I understand that the modulus of the gravitational fields must be equal, however I'm not quite able to understand the calculation of potential due to each portion.

I tried calculating the potential by considering differential rings and integrating over the angle subtended at the given point... but it gets very messy and is clearly out of my scope. Is there an analytical way to approach this problem?

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Qmechanic
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Gravitational potential due to a "cap" (a portion of a hollow sphere) at a given point

enter image description here

In this problem, I understand that the modulus of the electric fields must be equal; however I'm not quite able to understand the calculation of potential due to each portion.

I tried calculating the potential by considering differential rings and integrating over the angle subtended at the given point.. but it gets very messy and is clearly out of my scope. Is there an analytical way to approach this problem?