# A charge of #-2 C# is at the origin. How much energy would be applied to or released from a # 4 C# charge if it is moved from # (-7 ,1 ) # to #(4 ,-6 ) #?

A negative change in potential energy indicates a decrease in potential energy, which releases the energy.

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The energy applied to or released from a 4 C charge when moved from (-7, 1) to (4, -6) due to the presence of a -2 C charge at the origin can be calculated using the formula for electric potential energy:

U = k * (q1 * q2) / r

Where: U is the electric potential energy k is Coulomb's constant (8.99 × 10^9 N m²/C²) q1 and q2 are the charges (in coulombs) r is the distance between the charges (in meters)

First, we need to calculate the distance between the two charges using the distance formula:

Distance = √((x2 - x1)² + (y2 - y1)²)

Plugging in the coordinates, we get:

Distance = √((4 - (-7))² + ((-6) - 1)²) = √(11² + (-7)²) = √(121 + 49) = √170

Now, we can calculate the energy:

U = (8.99 × 10^9 N m²/C²) * ((-2 C) * (4 C)) / (√170 m) U ≈ -9.59 × 10^8 J

The negative sign indicates that energy is released from the 4 C charge as it moves from (-7, 1) to (4, -6) in the presence of the -2 C charge at the origin.

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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.

- Two charges of # -6 C # and # 4 C# are positioned on a line at points # -6 # and # 9 #, respectively. What is the net force on a charge of # -1 C# at # 1 #?
- A charge of #-2 C# is at the origin. How much energy would be applied to or released from a # 4 C# charge if it is moved from # (7 ,5 ) # to #(3 ,-9 ) #?
- A charge of #9 C# is passing through points A and B on a circuit. If the charge's electric potential changes from #15 J# to #9 J#, what is the voltage between points A and B?
- A charge of #7 C# is at the origin. How much energy would be applied to or released from a # 5 C# charge if it is moved from # (6, 18 ) # to #(-5 ,-2 ) #?
- What is the force, in terms of Coulomb's constant, between two electrical charges of #-45 C# and #-75 C# that are #15 m # apart?

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