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immortalsameer13
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scalar potential can be obtained by integrating the vector point function whose curl is zero but how to arrive at this result that a potential exist
Because the closed curve integral is zero, the one-way integral from one point to another has only one answer no matter which path is taken. So the one-way integral gives you a well-defined definition of the potential.immortalsameer13 said:scalar potential can be obtained by integrating the vector point function whose curl is zero but how to arrive at this result that a potential exist
A scalar potential is a mathematical function that assigns a scalar value to each point in space. It is used to describe the potential energy of a conservative force, such as gravity or electric fields.
If the curl of a vector point function is zero, it indicates that the vector field is conservative. This means that it can be expressed as the gradient of a scalar potential.
The proof involves showing that the vector field is irrotational, meaning that it has zero curl. This can be done using vector calculus techniques, such as the gradient, divergence, and curl operators.
If a scalar potential exists, it means that the vector field is conservative and can be described by a single scalar function. This simplifies calculations and allows for easier analysis of the field.
No, if the curl of the vector point function is not zero, it indicates that the vector field is non-conservative and cannot be described by a scalar potential. In this case, other mathematical techniques, such as line integrals, must be used to analyze the field.