1.How much work is required to move a single electron through a potential difference of 100.volts? *
1 point
- 1.6 x 102-21
b. 1.6 x 10 x 19
C. 1.6 x 10-17]
d. 1.0 x 10x2J
2.How much electrical energy is required to move a 4.00-microcoulomb
I point charge through a potential difference of 36.0 volts?
α. 9.00 x 10 x 61
b. 144 J
C. 3.44 x 10-4.3
d. 111 x 10-71
The Correct Answer and Explanation is :
Question 1:
To calculate the work done to move a single electron through a potential difference, we use the formula for electric work:
[
W = q \times V
]
Where:
- ( W ) is the work in joules (J),
- ( q ) is the charge of the electron, which is approximately ( 1.6 \times 10^{-19} \, \text{C} ),
- ( V ) is the potential difference in volts.
Given:
- ( q = 1.6 \times 10^{-19} \, \text{C} ),
- ( V = 100 \, \text{V} ),
Now, substituting the values:
[
W = (1.6 \times 10^{-19} \, \text{C}) \times (100 \, \text{V}) = 1.6 \times 10^{-17} \, \text{J}
]
Thus, the work required to move a single electron through a potential difference of 100 volts is ( 1.6 \times 10^{-17} \, \text{J} ), which corresponds to answer C.
Question 2:
To calculate the electrical energy required to move a 4.00-microcoulomb charge through a potential difference, we use the same formula:
[
W = q \times V
]
Where:
- ( W ) is the work in joules (J),
- ( q ) is the charge in coulombs,
- ( V ) is the potential difference in volts.
Given:
- ( q = 4.00 \, \mu C = 4.00 \times 10^{-6} \, \text{C} ),
- ( V = 36.0 \, \text{V} ),
Now, substituting the values:
[
W = (4.00 \times 10^{-6} \, \text{C}) \times (36.0 \, \text{V}) = 1.44 \times 10^{-4} \, \text{J}
]
Thus, the energy required to move the 4.00-microcoulomb charge through a potential difference of 36.0 volts is ( 1.44 \times 10^{-4} \, \text{J} ), which corresponds to answer C.
Explanation:
In both cases, the work (or energy) required to move a charge through a potential difference is directly related to the amount of charge and the voltage. The higher the charge or the potential difference, the more energy is required. This is a fundamental concept in electrostatics, where the work done to move a charge in an electric field is proportional to both the magnitude of the charge and the potential difference (voltage) the charge is moved through. The energy is measured in joules, where one joule is the energy required to move a charge of one coulomb through a potential difference of one volt.