To understand the relationship and differences between electric potential and el

Question

To understand the relationship and differences between electric potential and electric potential energy.

In this problem we will learn about the relationships between electric force F , electric field E , potential energy U, and electric potential V. To understand these concepts, we will first study a system with which you are already familiar: the uniform gravitational field.

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. Be sure to use the hints if you don't remember how to derive potential energy from an expresson for force.

Express U(z) in terms of q, E, and z.

U(z) =

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

Find the electric potential V of the uniform electric field E =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.

Express V in terms of q, E, and z.

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

Choose the appropriate answer combination to fill in the blanks correctly.

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

Choose the appropriate answer combination to fill in the blanks correctly.

upward downward upward or downward depending on its charge downward only if the ratio of qE to initial velocity is large e

Explanation / Answer

Ans:-

Given data

h =z

Potential energy U(z) = mgh

                                                = F*z

But F =q*E

U(Z) = qEz

# the charged particle accelerate when released with upward initial velocity – upward or downward depending on its charge

# Electric potential V is defined by the relationship U = qV

V = U/q = qEz /q

V = - Ez

#A positive test charge will accelerate toward regions of lower electric potential and lower electric potential energy.

#A negative test charge will accelerate toward regions of higher electric potential and lower electric potential energy.

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