Question

You stand at location A, a distance d from the origin, and hold a small charged ball. You find that the electric force on the ball is 0.08 N. You move to location B, a distance 2d from the origin, and find the electric force on the ball to be 0.04 N. What object located at the origin might be the source of the field? (1) A point charge, (2) A dipole, (3) A uniformly charged rod, (4) A uniformly charged ring, (5) A uniformly charged disk, (6) A capacitor, (7) A uniformly charged hollow sphere, (8) None of the above If the force at B were 0.0799 N, what would be your answer? If the force at B were 0.01 N, what would be your answer? If the force at B were 0.02 N, what would be your answer?

Short answer

The answers are given below,

• If the force at B is\(0.04\;{\rm{N}}\)then the answer is (8).
• If the force at B is\(0.0799\;{\rm{N}}\)then the answer is (8).
• If the force at B is\(0.01\;{\rm{N}}\)then the answer is (2).
• If the force at B is \(0.02\;{\rm{N}}\) then the answer is (1) and (7).

Step-by-step solution

Identification of given data

The given data can be listed below,

• The electric field on the ball at the location Ais, $\mathrm{F}=0.08\mathrm{N}$
• The electric force at distance 2d at the location B is,${\mathrm{F}}_2=0.04\mathrm{N}$

Concept/Significance of a dipole.

A dipole is anything that has two opposing poles in general. Magnetic North and South poles, for example, are equal and opposing. An electric dipole, like a magnet, has two equal and opposite electric charges, one positive and one negative.

Determination of whether object located at the origin might be the source of the field or not.

The relation between the electric field of given 7 objects and radial distance is given by,

1) For point charge,4

$E_P\infty \frac{1}{r^3}$

2) For dipole,

$E_P\infty \frac{1}{{r^3}_{}}$

3) For uniformly charged rod,

$E\infty \frac{1}{r\sqrt{{\left(r\right)}^2}+{(L/2)}^2}$

4) For uniformly charged ring,

$E\infty \frac{r}{{(r^2+R^2)}^{3/2}}$

5) For uniformly charged disk,

$E\infty \left(1-\frac{r}{\sqrt{r^2+R^2}}\right)$

1. The capacitor shows no relation with distance.
2. The hollow sphere have the same relation as point charge.

Since we are looking for a charged object, that shows a linear inverse radial distance dependence for the electric field exerted on the small charged ball shows the corresponding decrease in value, clearly none of the 7 above stated object shows the required relation dependence, and hence the answer is (8) . , if we examine object number (3) carefully under the approximation that the radial distance is so much greater than the length of the rod, such that the equation of the electric field produced by such rod will be

role="math" localid="1656934937415" $E\mathit{}\mathit{=}\frac{\mathit{2}\mathit{K}\mathit{Q}}{\mathit{L}\mathit{r}}$

Thus, there is not enough information about the nature of the numbers (8) is the best correct answer in this case, but if given that the radial distance is so much greater than the length of the rod then (3) would be a correct answer.

It is given that the force at B is 0.0799 then we are looking for almost a constant electric field, i.e., a source that shows no dependence on the distance. None of the 7 stated sources electric fields shows independence on the radial distance, except for the capacitor (6) but that would implies that the distance and are inside a very small gap between the two plates of a capacitor, which doesn't very reasonable answer as a person moving gives a sense of somebody moving something at least of centimeters if not meters and usually the gab in the order of mm for an ordinary sized capacitor or else we would have a very gigantic capacitor thus we can safely say that this is not a correct answer. And the electric field in the vicinity very near to a disk i.e. (5) providing that the which means that the disk have a radius much greater than And, as the lack the geometric description for the value of the numbers it can be safely say that the best answer would be none of the above (8).

If the object at location B have a force of 0.01 N, then is a little bit straight forward, as the we are looking for some source that shows a cubic inverse radial distance dependence as that of the dipole. Thus, the answer is (2) A dipole.

If the object at location B have a force of 0.02 N, then for a source whose electric field shows square inverse radial distance dependence, which are given by both (1) A point charge and (7) A uniform charged hollow sphere.