# A charge of #-1 C# is at the origin. How much energy would be applied to or released from a # 3 C# charge if it is moved from # (-5 ,1 ) # to #(2 ,-6 ) #?

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The energy applied to or released from a charge when it is moved in an electric field can be calculated using the formula:

[ W = q \Delta V ]

Where:

- ( W ) is the energy,
- ( q ) is the charge, and
- ( \Delta V ) is the change in electric potential.

First, we calculate the change in electric potential (( \Delta V )) between the two points using the formula:

[ \Delta V = V_f - V_i ]

Where:

- ( V_f ) is the final electric potential, and
- ( V_i ) is the initial electric potential.

Given that the charge at the origin is -1 C and the charge at the final position is 3 C, we can find the electric potential at each point using the formula for electric potential due to a point charge:

[ V = \frac{k \cdot q}{r} ]

Where:

- ( k ) is Coulomb's constant (( 8.99 \times 10^9 , \text{N}\cdot\text{m}^2/\text{C}^2 )),
- ( q ) is the charge, and
- ( r ) is the distance from the point charge to the point where the electric potential is being calculated.

Using this formula, we can find ( V_i ) at the initial point (-5, 1) and ( V_f ) at the final point (2, -6).

After finding ( \Delta V ), we can use the formula for energy to calculate the energy applied to or released from the 3 C charge when it is moved between the two points.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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