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A point charge with a charge q1 =2.90μC is held stationary at the origin. A second point charge with a charge q2=−4.90μC moves from the point x=0.110 m,y=0 to the point x=0.250 m,y=0.250 m You may want to review (Page) For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Conservation of energy with electric forces. How much work is done by the electric force on q2?

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Final answer:

The work done by the electric force on a second point charge as it moves from one point to another in the electric field of a stationary charge is the change in electric potential energy, calculated using Coulomb's law and the change in distance between the charges.

Step-by-step explanation:

To calculate the work done by the electric force on charge q2 (-4.90µC) as it moves within an electric field created by charge q1 (2.90µC), we can use the concept of electric potential energy. Work done by the electric force in moving a charge from point A to B is equal to the change in electrical potential energy, ΔU, and can be calculated using the formula:

W = U_A - U_B

Where:

  • U_A is the initial electric potential energy at point A (x=0.110 m, y=0)
  • U_B is the final electric potential energy at point B (x=0.250 m, y=0.250 m)

The electric potential energy is given by:

U = k*q1*q2/r

Where:

  • k is Coulomb's constant (8.988×109 N*m2/C2)
  • r is the distance between two charges

For point A, the distance r_A is 0.110 m, and for point B, we have to calculate r_B using the Pythagorean theorem since the charge moves diagonally to (0.250 m, 0.250 m), which gives r_B = √((0.2502) + (0.2502)) m. After calculating r_B and plugging all values into the formula, we can find the work done by the electric force on q2.

Remember, since the potential energy at point B will be less due to greater distance between charges (higher r_B), the work done (W) on q2 is expected to be negative, indicating that the electric force is doing work to move the charge further from q1.

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