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Today I'm going to work with you on a new concept and that is the concept of what we call electric field.

We spend the whole lecture on electric fields.

If I have a — a charge, I just choose Q, capital Q and plus at a particular location and at another location I have another charge little Q, I think of that as my test charge.

And there is a separation between the two which is R.

The unit vector from capital Q to li- little Q is this vector.

And so now I know that the two charges if they were positive — let's suppose that little Q is positive, they would repel each other.

Little Q is negative they would attract each other.

And let this force be F and last time we introduced Coulomb's law that force equals little Q times capital Q times Coulomb's constant divided by R squared in the direction of R roof.

The two have the same sign.

It's in this direction.

If they have opposite sign it's in the other direction.

And now I introduce the idea of electric field for which we write the symbol capital E.

And capital E at that location P where I have my test charge little Q, at that location P is simply the force that a test charge experienced divided by that test charge.

So I eliminate the test charge.

So I get something that looks quite similar but it doesn't have the little Q in it anymore.

And it is also a vector.

And by convention, we choose the force such that if this is a positive test charge then we say the E field is away from Q if Q is positive, if Q is negative the force is in the other direction, and therefore E is in the other direction.

So we adopt the convention that the E field is always in the direction that the force is on a positive test charge.

What you have gained now is that you have taken out the little Q.

In other words, the force here depends on little Q.

Electric field does not.

The electric field is a representation for what happens around the charge plus Q.

This could be a very complicated charge configuration.

An electric field tells you something about that charge configuration.

The unit for electric field you can see is newtons divided by coulombs.

In SI units and normally we won't even indicate the — the unit, we just leave that as it is.

Now we have graphical representations for the electric field.

Electric field is a vector.

So you expect arrows and I have here an example of a — a charge plus three.

So by convention the arrows are pointing away from the charge in the same direction that a positive test charge would experience the force.

And you notice that very close to the charge the arrows are larger than farther away.

That it, that sort of represents- is trying to represent- the inverse R square relationship.

Of course it cannot be very qualitative.

But the basic idea is this is of course spherically symmetric, if this is a point charge.

The basic idea is here you see the field vectors and the direction of the arrow tells you in which direction the force would be, if it is a positive test charge.

And the length of the vector give you an idea of the magnitude.

And here I have another charge minus one.

Doesn't matter whether it is minus one coulomb or minus microcoulomb.

Just it's a relative representation.

And you see now that the E field vectors are reversed in direction.

They're pointing towards the minus charge by convention.

We spend the whole lecture on electric fields.

If I have a — a charge, I just choose Q, capital Q and plus at a particular location and at another location I have another charge little Q, I think of that as my test charge.

And there is a separation between the two which is R.

The unit vector from capital Q to li- little Q is this vector.

And so now I know that the two charges if they were positive — let's suppose that little Q is positive, they would repel each other.

Little Q is negative they would attract each other.

And let this force be F and last time we introduced Coulomb's law that force equals little Q times capital Q times Coulomb's constant divided by R squared in the direction of R roof.

The two have the same sign.

It's in this direction.

If they have opposite sign it's in the other direction.

And now I introduce the idea of electric field for which we write the symbol capital E.

And capital E at that location P where I have my test charge little Q, at that location P is simply the force that a test charge experienced divided by that test charge.

So I eliminate the test charge.

So I get something that looks quite similar but it doesn't have the little Q in it anymore.

And it is also a vector.

And by convention, we choose the force such that if this is a positive test charge then we say the E field is away from Q if Q is positive, if Q is negative the force is in the other direction, and therefore E is in the other direction.

So we adopt the convention that the E field is always in the direction that the force is on a positive test charge.

What you have gained now is that you have taken out the little Q.

In other words, the force here depends on little Q.

Electric field does not.

The electric field is a representation for what happens around the charge plus Q.

This could be a very complicated charge configuration.

An electric field tells you something about that charge configuration.

The unit for electric field you can see is newtons divided by coulombs.

In SI units and normally we won't even indicate the — the unit, we just leave that as it is.

Now we have graphical representations for the electric field.

Electric field is a vector.

So you expect arrows and I have here an example of a — a charge plus three.

So by convention the arrows are pointing away from the charge in the same direction that a positive test charge would experience the force.

And you notice that very close to the charge the arrows are larger than farther away.

That it, that sort of represents- is trying to represent- the inverse R square relationship.

Of course it cannot be very qualitative.

But the basic idea is this is of course spherically symmetric, if this is a point charge.

The basic idea is here you see the field vectors and the direction of the arrow tells you in which direction the force would be, if it is a positive test charge.

And the length of the vector give you an idea of the magnitude.

And here I have another charge minus one.

Doesn't matter whether it is minus one coulomb or minus microcoulomb.

Just it's a relative representation.

And you see now that the E field vectors are reversed in direction.

They're pointing towards the minus charge by convention.

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