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The potential energy of a two particle s...

The potential energy of a two particle system separated by a distance `r` is given by `U(r ) =A/r` where A is a constant. Find to the radial force `F_(r)`, that each particle exerts on the other.

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To find the radial force \( F_r \) that each particle exerts on the other, we start with the given potential energy function: \[ U(r) = \frac{A}{r} \] where \( A \) is a constant and \( r \) is the distance between the two particles. ### Step 1: Understand the relationship between force and potential energy The force \( F \) associated with a potential energy \( U \) is given by the negative gradient of the potential energy with respect to distance. Mathematically, this is expressed as: \[ F = -\frac{dU}{dr} \] ### Step 2: Differentiate the potential energy function Now, we need to differentiate \( U(r) \) with respect to \( r \): \[ U(r) = \frac{A}{r} \] Using the power rule for differentiation, we can rewrite \( \frac{A}{r} \) as \( A r^{-1} \). The derivative is: \[ \frac{dU}{dr} = A \cdot (-1) \cdot r^{-2} = -\frac{A}{r^2} \] ### Step 3: Substitute the derivative into the force equation Now, we substitute the derivative back into the force equation: \[ F = -\left(-\frac{A}{r^2}\right) = \frac{A}{r^2} \] ### Conclusion Thus, the radial force \( F_r \) that each particle exerts on the other is: \[ F_r = \frac{A}{r^2} \]
To find the radial force \( F_r \) that each particle exerts on the other, we start with the given potential energy function: \[ U(r) = \frac{A}{r} \] where \( A \) is a constant and \( r \) is the distance between the two particles. ...
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