Question

The Equation: is often used to calculate the electric potential from a point charge at an observation location. If we were to write this as a potential difference, we might write it as the potential difference from the observation to a point infinitely far away: The difference, Δν· is the quantity we can actually measure in the real world this is done by calibrating a voltage-measuring device to a location, and then moving elsewhere and reading off the difference in voltage. Suppose there is a point charge of 3.73 mC at the origin and our observation point is at0,4.31, 3.06 > m. The voltage-measuring device has already been calibrated, and we measure a voltage at the observation point of 8.31 MV. What would the device read for the voltage at a point infinitely far away from the charge?

Answer 1

Theoretically the voltage at a point infinitely far away from the charge will be zero.

According to the question, the point charge of 3.73 mC is placed at the origin and the observation point is at (0, 4.31, 3.06).

So, we can calculate the potential difference by using the relation :

  

Here, q = 3.73 mC

and    (distance of observation point from origin)  

r02 +4.312 + 3.062- V27.9397- 5.285 m

So,   

or,   

▲V 6.31 x 106 V-6.31 MV

This is the potential difference at observation point.

But the measured value of potential difference using calibration device is 8.31 MV.

So, the error in measurement = 8.31 - 6.35 = 2MV (also known as zero point error)

Hence, the device will read nearly 2 MV at a point infinitely far away from the charge.

For any doubt please comment.