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Course: Electrical engineering>Unit 5

Lesson 2: Fields, potential, and voltage

Proof: Field from infinite plate (part 1)

Advanced proof of the formula for the electric field generated by a uniformly charged, infinite plate. Created by Sal Khan.

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• Around , Sal says that the force generated by the ring is = kqq/d^2. However, how is the entire charge of the ring enclosed to one point? More specifically, how come he is treating the entire charge of the ring as enclosed to one point? Is he allowed to do that? Thanks.
• Since the ring is of uniform charge, and the charge density is sigma then Q (<-Charge of ring) = sigma (<-charge density) * (2 * pi * r * dr) (<-area of the ring). He is correct in doing this, but only in the case of a surface of uniform charge (The charge at every point of the surface is equal) and with the test charge (q) at the center of the ring so that all of the horizontal components of the electrostatic forces cancel, leaving only the vertical components.

Since forces are vector quantities and in the same direction, we can treat them as if they were all directly under the test charge and them sum them up to receive the total net force on the test charge from the ring.

Now if the ring was not of uniform charge and/or the test charge was not at the center of the ring, then we would have a much more difficult problem.

I hope this clears things up for you. ^^
• Why does Sal take an infinite plane? I find it quite hard to imagine.
• If you pick a plane of finite size, you would have to compute the net effect of whatever you are studying at that boundary and include it in your final answer. In much of physics, an effect (gravitational potential or electric field for examples) are defined as zero at infinity, so you can ignore that 'boundary' value.

So think of it as 'choose a plane whose size is large enough that we can use infinity as the 'far' distance (for example, we could calculate (or integrate) from zero radius to infinity). If the effect has dropped to zero at infinity, that term becomes simpler to calculate - or may drop out altogether.
• He saying i need to learn about calculus first, can anybody tell me from where should i start learning it, i mean there are 3 different calculus topics ;Differential, multivariable, integral.Or any other type?
• For this specific video, you'd want to learn basic integration techniques, though learning most of differential and integral calculus (single-variable) would be a good idea so as to establish a thorough knowledgebase.
• So, a test charge could be light-years away and still feel the same force?
• If the plate were infinite, yes. Infinite is big even compared to light-years. But there's no such thing as an infinite plate, right?
• Why do you calculate the charge from the whole area, if youre only gonna use the points on the edge of the circle?
• since it is a ring and ring does not has a symmetry except at the ends of diameter, therefore he has taken two small charges 'dq' and then integrate it
• I still don't get what exactly is Gauss law used for. Yes, it's for calculating electric fields(?) but don't we have Coulomb's Law to calculate that?
(1 vote)
• Coulomb's Law allows you to calculate the field from a point charge. Gauss's Law lets you calculate the field from any arbitrary distribution of charges. Technically you could use Coulomb's Law for everything, but it would be extremely difficult calculating the field from trillions of charges and summing them all up. Gauss's Law just makes solving for that type of problem much easier.
• hello,
can some one tell me what is SOHCAHTOA at ??