Visualizing E-field

1. Linearization

Since for the second part,

,

we can rewrite it as

.

Then we can plot V as y and ln(r) as x to get a linear relationship.

---------

Can we plot e^V as y and r as x? The answer is no. The above equation can be rewritten as

,

so the linear relationship is between e^V and r^a, not r.

2. Uncertainty of V

Based on the reference material on Blackboard, when the range is 4V, the uncertainty should be calculated from

0.8%V + 1dgt,

which means that if your reading is V, then the uncertainty is

0.8%*V + 1*the unit of least significant digit.

Example:

For V = 3.142 Volt,

,

therefore, after correct rounding, V should be expressed as

.

3. Uncertainty of ln(r)

From error propagation formula,

.

Example:

For r = 11 mm, we have

,

and

.

Thus

.

4. Testing the Linear Relationship

Since we are only making an analogy of the electric field using current, we cannot determine the charge. The linear relationship can still be tested, however you must report the R² statistic.

5. Uncertainties

If you change the orientation angle of the probe of the Digital Multimeter, you can see some difference in the reading, and that is the major uncertainty in this lab.

6. Lines doe not have zero y-intercept?

Think about why, we will talk about this in our next lab.