Consider two thin disks, of negligible thickness, of radiusR oriented perpendicular to thex axis such that the x axis runs throu
gh thecenter of each disk. The disk centered at x=0 has positive charge density eta, and the disk centered at x=a has negative charge density -\eta, where the charge density is charge perunit area. What is the magnitude E of the electric field at the point on thex axis with x coordinate a/2? For what value of the ratio R/a of plate radius to separation between the plates does the electric field at the point x=a/2 on the x axis differ by 1 percent from the result η/ϵ for infinite sheets?
1 answer:
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Missing figure in the problem: https://www.physicsforums.com/attachments/p4-46-gif.117834/
Solution:
part a) The bucket is not moving so the resultant of the forces acting on it is zero. Let's apply the equation of equilibrium. We have:
so
where T=90.5 N is the tension of the rope, and a factor 2 is applied because the string holds the bucket twice. From this we find
part b) Here the situation is different: the string holds the bucket only in one point. Moreover, the bucket is pulled up at constant velocity, so zero acceleration: this means that the resultant of the forces acting on the bucket is zero. Therefore, the equation of equilibrium in this case is
and so, since we know from part a) that
, we can find the new tension T:
Solution:
part a) The bucket is not moving so the resultant of the forces acting on it is zero. Let's apply the equation of equilibrium. We have:
so
where T=90.5 N is the tension of the rope, and a factor 2 is applied because the string holds the bucket twice. From this we find
part b) Here the situation is different: the string holds the bucket only in one point. Moreover, the bucket is pulled up at constant velocity, so zero acceleration: this means that the resultant of the forces acting on the bucket is zero. Therefore, the equation of equilibrium in this case is
and so, since we know from part a) that