What is the value of r given the change in electric potential?

In summary: However, your solution would be more clear if you showed your steps and explained what you did. Also, it would be better to use variables for the unknowns, such as V(r) and V(r-1.5) instead of plugging in numbers.
  • #1
mrcotton
120
0
The electric potential at a distance r from a positive point charge is 45V. The potential
increases to 50 V when the distance from the charge decreases by 1.5 m. What is the
value of r?

A 1.3m
B 1.5m
C 7.9m
D 15m

Homework Statement



the answer is D

Homework Equations


V=(1/4∏ε) q/r
v proportional to 1/r

The Attempt at a Solution


5=(q/(1/4∏ε))*((1/r-1.5)-(1/r))

How embarrassing I just can’t get my head around this one. Am I setting the equation up correct to solve.
If I have I need desperate help with the algebra.
Thank you
 
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  • #2


mrcotton said:
The electric potential at a distance r from a positive point charge is 45V. The potential
increases to 50 V when the distance from the charge decreases by 1.5 m. What is the
value of r?

A 1.3m
B 1.5m
C 7.9m
D 15m

Homework Statement



the answer is D

Homework Equations


V=(1/4∏ε) q/r
v proportional to 1/r

The Attempt at a Solution


5=(q/(1/4∏ε))*((1/r-1.5)-(1/r))

How embarrassing I just can’t get my head around this one. Am I setting the equation up correct to solve.
If I have I need desperate help with the algebra.
Thank you
You have one equation and two unknowns.

Taking the ratio [itex]\displaystyle \ \ \frac{V(r)}{V(r-1.5)}\ \ [/itex] might be more helpful.

Otherwise, use your equation along with [itex]\displaystyle \ \ V(r)=45=\frac{q}{4\pi\epsilon_0\,r}\ \ [/itex] then eliminate q & solve for r.
 
  • #3


You're going to want to get rid of the constants you don't have values for (like the charge value q) so you'll probably want to set it up as a ratio so that they'll cancel out.

EDIT: SammyS got their first!
 
  • #4


Thank you guys.
I did it like this with your help.
Is this mathematicaly sound.
Thanks
Mr C
electrostaic_zpsf9de5785.jpg
 
  • #5


mrcotton said:
Thank you guys.
I did it like this with your help.
Is this mathematically sound.
Thanks
Mr C
attachment.php?attachmentid=54562&stc=1&d=1357706512.jpg
That answer is correct.
 

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FAQ: What is the value of r given the change in electric potential?

What is the scaling problem with potential difference change and calculation of original length?

The scaling problem refers to the difficulty in accurately measuring the original length of an object when there is a change in potential difference, or voltage, applied to it. This is due to the fact that the length of an object can change when an electric current is passed through it, making it challenging to determine the object's original length.

2. How does potential difference affect the length of an object?

When an electric current is passed through an object, it can cause a change in the object's length. This is due to the fact that the atoms in the object are being pushed or pulled by the electric current, causing them to either expand or contract, resulting in a change in the object's length.

3. Why is it important to accurately calculate the original length of an object?

Calculating the original length of an object is important in order to ensure precision and accuracy in scientific experiments and measurements. The original length serves as a baseline for comparison and allows for proper analysis and understanding of the object's behavior under different conditions.

4. What factors can contribute to the scaling problem with potential difference change?

There are several factors that can contribute to the scaling problem, including the material and composition of the object, the amount of current passing through it, and the duration of the current flow. Additionally, any external factors such as temperature and pressure can also impact the object's length and contribute to the scaling problem.

5. How can the scaling problem be minimized or avoided?

One way to minimize the scaling problem is by using materials with low resistance, as they will experience less change in length when an electric current is passed through them. Another approach is to use precise measurement techniques, such as using a micrometer, to accurately measure the length of an object. Additionally, controlling external factors like temperature and pressure can also help minimize the scaling problem.

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