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[Ras12]

Homework Statement

Finding magnitude of electric field. Thank you for any help!! For some reason I just cannot grasp this concept.

Relevant Equations

E=k((q1*q2)/r^2)
lambda= Q/L

 

[archaic]

Well, about the concept, Coulomb experimentally determined that the force of interaction between two charges has a magnitude of $k\frac{qQ}{r^2}$, where $k$ is a constant, $r$ is the distance between them, and $q$ and $Q$ are respectively the charges' "charges".

One then imagines this: If I have just one charge, $Q$, then I can imagine that it creates a "field" such that if I place another charge anywhere, then the force between the two would be as already mentioned.

That field would have a magnitude of $E=\frac{F}{q}=k\frac{Q}{r^2}$, where we, now, interpret $r$ as the distance to any given point in space, thus you have a function of position.

In vector form, you would have $\vec E(x, y, z)=k\frac{Q}{(Q_x-x)^2+(Q_y-y)^2+(Q_z-z)^2}\vec u$, where $\vec u$ is the unit vector of the line connecting the "fixed" charge (the one "generating" the field) and the point $(x, y, z)$, and $Q_i$ are the charge's coordinates.

For your exercise, you need to consider another fact, which is that you can add fields, so that if you have $n$ charges, then the electric field at any point is the sum of all electric field. You can also consider infinitesimal charges, i.e infinitely small parts of a "total" charge.

The wire is your "total" charge, you need to consider it being formed of infinitely many infinitesimal charges $dq$, and that the magnitude of the field generated by any of these is $k\frac{dq}{r^2}$.
This a really watered down summary of your lecture, you should go read the textbook and look at examples. I recommend Michel van Bizen's channel. Here's a link to the chapter you are currently studying.

 

[haruspex]

It's very similar to a gravitational field. At a given position in space the force it exerts on a charge is proportional to the value of that charge, just as Earth's pull on a mass is proportional to the magnitude of the mass. And as with a gravitational field, if you go twice as far from the field's source the strength of the field is one quarter; and in both cases, the field has a direction as well as a strength (magnitude) at each point in space.

The main difference is that in gravitation masses are all positive and attract each other, whereas in electricity we have positive and negative charges, with opposites attracting and likes repelling.