What is wrong with Figure 15.35 and this associated incorrect student explanation? “The electric field at location inside the uniformly charged sphere points in the direction shown, because the charges closest to this location have the largest effect.” (Spheres provide the most common exception to the normally useful rule that the nearest charges usually make the largest contribution to the electric field.)

Short Answer

Expert verified

The wrong fact about the given figure is the direction of the electric field at the location that is directed outward, but the electric field is zero.

Step by step solution

01

Significance of the electric field

The electric field is referred to as a region which allows a charged particle to exert a particular force on another charged particle.

The equation of the electric field gives the answer that is wrong with the figure.

02

Identification of the problem with the figure

It can be observed from the given figure that the negative charge outside the sphere is uniformly distributed and the other negative charges are further away, due to the excessive amount of the negative charges. The electric field at the location and the negative charges outside the spheres cancels each other. So, the electric field becomes zero. Hence, the direction of the electric field cannot be outward as it has zero value.

Thus, the wrong fact about the given figure is the direction of the electric field at the location that is directed outward, but the electric field is zero.

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Most popular questions from this chapter

A plastic rod 1.7mlong is rubbed all over with wool, and acquires a charge of-2×10-8C(Figure 15.52). We choose the center of the rod to be the origin of our coordinate system, with the x axis extending to the right, the y axis extending up, and the z axis out of the page. In order to calculate the electric field at locationA=<07,0,0>, we divide the rod into eight pieces, and approximate each piece as a point charge located at the center of the piece.

(a) What is the length of one of these pieces? (b) What is the location of the center of piece number 3? (c) How much charge is on piece number? (Remember that the charge is negative.) (d) Approximating piece 3as a point charge, what is the electric field at location A due only to piece 3? (e) To get the net electric field at location A, we would need to calculatedue to each of the eight pieces, and add up these contributions. If we did that, which arrow (a–h) would best represent the direction of the net electric field at location A?

If the magnitude of the electric field in air exceeds roughly3×10-6N/C, the air breaks down and a spark forms. For a two-disk capacitor of radius50cmwith a gap of role="math" localid="1656068507772" 1mm, what is the maximum charge (plus and minus) that can be placed on the disks without a spark forming (which would permit charge to flow from one disk to the other)? Under these conditions, what is the strength of the fringe field just outside the center of the capacitor?

If the total charge on a thin rod of length0.4mis 2.5n/C, what is the magnitude of the electric field at a location1Cmfrom the midpoint of the rod, perpendicular to the rod?

A clear plastic pen 12 cmlong is rubbed all over with wool, and acquires a negative charge of -2nC. You want to figure out the electric field a distance of 18 mmfrom the pen, near the middle of the pen. (a) You decide to model the pen as a rod consisting of a series of five segments, each of which you will consider to be approximately point-like. What is the length of each segment in meters? (b) What is the amount of charge Qon each of the five segments? (c) In general, if the rod has a length Land total charge Q, and you divide the rod into Nsegments, what is the amount of chargeQon each piece? (d) If the length of each segment is dL, write a symbolic expression for the number of pieces Nin terms of the length of the rod Land the length of one piece dL.(e) Now write a symbolic expression for the amount of charge on each piece in terms of the length of the rod and the length of a small piece.

Question: Breakdown field strength for air is roughly . If the electric field is greater than this value, the air becomes a conductor. (a) There is a limit to the amount of charge that you can put on a metal sphere in air. If you slightly exceed this limit, why would breakdown occur, and why would the breakdown occur very near the surface of the sphere, rather than somewhere else? (b) How much excess charge can you put on a metal sphere of radius without causing breakdown in the neighboring air, which would discharge the sphere? (c) How much excess charge can you put on a metal sphere of onlyradius? These results hint at the reason why a highly charged piece of metal tends to spark at places where the radius of curvature is small, or at places where there are sharp points.

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