Mastering Physics: Electric Potential Energy versus Electric Potential

Mastering Physics: Electric Potential Energy versus Electric Potential

Part A

Question: Find the force F⃗ (z) on an object of mass m in the uniform gravitational field when it is at height z=0.

Answer: F⃗ (z) =  −mgk^

Part B

Question: Now find the gravitational potential energy U(z) of the object when it is at an arbitrary height z. Take zero potential to be at position z=0. Keep in mind that the potential energy is a scalar, not a vector.

Answer: U(z) =  mgz

Part C

Question: In what direction does the object accelerate when released with initia…

Answer: downward

Part D

Question: Find F⃗ (z), the electric force on the charged particle at height z.

Answer: F⃗ (z) =  −qEk^

Part E

Question: Now find the potential energy U(z) of this charged particle when it is at height z. Take zero potential to be at position z=0.

Answer: U(z) =  qEz

Part F

Question: In what direction does the charged particle accelerate when released with upward initial velocity?

Answer: upward or downward depending on its charge

Part G

Question: Find the electric potential V of the uniform electric field E⃗ =Ek^. Note that this field is not pointing in the same direction as the field in the previous section of this problem. Take zero potential to be at position z=0.

Answer: V =  −Ez

Part H

Question: Find an expression for the electric field E⃗  in terms of the derivative of V.

Answer: E⃗  =  (−dV/dz) × k^

Part I

Question: A positive test charge will accelerate toward regions of ________ electric potential and ________ electric potential energy.

Answer: lower; lower

Part J

Question: A negative test charge will accelerate toward regions of ________ electric potential and ________ electric potential energy.

Answer: higher; lower