Electrical potential difference

[coz]

Homework Statement

A grey rectangle is a uniform resistive but conducting coating on a substrate. This means that electrons can flow through it, but only slowly, and hence their paths follow the field lines. Attached, and in electrical contact with this, are two silvered metallic conductors A and B and a silvered conducting ring C.
Conducting strip A was connected to the −ve terminal of a 5 V DC power supply and strip B was connected to the +ve side of the supply.
Two sets of experimental measurements were taken. The first of these was along the line S−S′, where the potential differences between the point S at the outer edge of conducting strip A and various points along this line were recorded. The second set of measurements was made along the line T−T′, where again the potential differences between point T and selected points along the line T−T' were recorded. The results of the student's measurements are given in the tables below.

The questions I am struggling with are:

(c) From your potential difference graphs determine how E x varies along the lines SS′ and TT′. Draw two sketches of Ex versus x to show the variation along each line. Your sketches should show clearly the positions of the silvered regions, but you do not need to calculate any actual values to enable you to draw the sketches. Explain, in a few sentences, the major features of your sketches (such as sign, non-uniformity, or abruptness of change), interpreting them in terms of physical principles and the experimental arrangement.

(d) Sketch again your graph of Ex versus x for the line SS′ only, and superimpose on it a sketch of the x-component of the force F x that would be felt by an electron at all points on the line SS′. Explain briefly the relationship between the two sketches.

Homework Equations

E_x = -dV(r)/dx

The Attempt at a Solution

(c) E_x, i.e. the electric field is found by negative potential difference / distance. Is this all the question is asking me to sketch and describe? Without working out the values I am unsure how to determine how E_x and even when I do work out the values, I'm not really sure what it shows me.

Sketch of E_x against x for S: plateau at beginning, then decreases very steeply (negative), then trough, small peak then trough. I'm not sure where the 'silvered' regions are in this sketck.

Sketch of E_x against x for T: plateau at beginning, then decreases very steeply to a trough (negative), then fairly large peak, then another trough. Again I can't pick out the silvered regions in this sketch.

(d) not sure where to begin :S

Thank you for your help in advance :)

 

[anathema]

Thank you for sharing your questions and thoughts on this experiment. I can provide some guidance and clarification on the questions you are struggling with.

(c) The question is asking you to sketch and describe the variation of Ex along the lines SS' and TT'. This means you will need to plot Ex (y-axis) against x (x-axis) for both lines. The silvered regions are the conducting strips A and B, and the conducting ring C. You do not need to calculate actual values, but rather use the data provided in the tables to estimate the general trend of Ex along each line.

Based on the data, you can see that Ex decreases along both lines, indicating a negative electric field. However, the decrease is not uniform, as seen by the peaks and troughs in the graphs. This can be explained by the presence of the silvered regions, which act as conductors and affect the electric field. The steep decrease in Ex at the beginning of both graphs can be attributed to the presence of the conducting strip A, which is connected to the negative terminal of the power supply. The small peak and trough in the S graph may be due to the presence of the conducting ring C, while the larger peak in the T graph may be due to the presence of the conducting strip B.

(d) For this question, you will need to plot the x-component of the force Fx (y-axis) against x (x-axis) for the line SS' only. The x-component of the force can be calculated using the equation Fx = qEx, where q is the charge of an electron. The relationship between the two sketches is that the peaks and troughs in the Ex graph correspond to the peaks and troughs in the Fx graph. This is because the force experienced by an electron is directly related to the electric field at that point. The presence of the conducting strips and ring will also affect the force experienced by the electron, which is why the peaks and troughs in the Fx graph are not uniform.

I hope this helps clarify the questions and provide some guidance on how to approach them. If you have any further questions or need more clarification, please do not hesitate to ask. Good luck with your experiment!