You are the captain of a spaceship. You need to measure the electric field at a specified location P in space outside your ship. You send a crew member outside with a meter stick, a stopwatch, and a small ball of known mass M and net charge +Q (held by insulating strings while being carried). (a) Write down the instructions you will give to the crew member, explaining what observations to make. (b) Explain how you will analyze the data that the crew member brings you to determine the magnitude and direction of the electric field at location P.

Since the equipment is the crew member, let’s call him A carries a stop watch, a meter stick with him, he can measure distance and time.

Since, I know the force experienced by a charge in field E is given by F = QE, which is in direction of the field E on the positive charge. And I know that the

F = ma. I am going to give following instruction to A.

i. Release the charged particle at point P, then catch as it moves a little.

ii. Align you meter stick along the direction the particle moved.

iii. Again release the particle at end of the meter stick and start the stopwatch, stop both (the particle and the stopwatch) as the particle reaches the other end and note the same.

iv. Repeat the steps as many time as reasonably possible.

Analysis of information brought by A, the direction to which the particle moves is the direction of field.

I’ll take the average of the readings of time noted by A, let’s call it ‘t’ .

Since initial velocity of the particle is u = 0, I’ll use to equation.

$$\begin{gathered} S=\frac{ut+a{t}^2}{2} \\ =\frac{a{t}^2}{2} \end{gathered}$$

S = length of the meter stick.

From the above equation I’ll know the acceleration of the particle.

From F = ma, it is fairly reasonable to assume that the forces other than the electric force are zero,

so$\to F=F_{net}$

$$\begin{gathered} QE=ma \\ E=\frac{ma}{Q} \end{gathered}$$

I knew mass m, charge Q, and I have calculated acceleration a fairly accurately, I know the magnitude of the electric field E.