Transcript Goal: To understand what Electric Fields are

Goal: To understand what
Electric Fields are and how to
calculate them.
Objectives:
1) Understanding what charges are.
2) Knowing how to produce a charge.
3) How to calculate an electric field
from a collection of charges
What is charge?
• For the most part, charge is a measure of
how many protons or electrons you have
somewhere.
• Charge is measured in units of Coulombs
(C).
• An elementary charge from a proton or
electron has magnitude of 1.602 * 10-19 C.
• Like charges repel. Opposite attract.
• Charges can move.
How do you get charge?
• 1) Rubbing (static electricity)
• 2) Induction (charge obtained from a
changing magnetic field)
• 3) Conduction (moving charge along a
wire)
Electric Field
• Suppose you wanted to know where the
water would flow when it rains.
• How would you do that?
Fields
• Fields are just a listing of possible
potential at any given point.
• For rain you look at the Gravitational Field
– which is just a fancy way of saying the
topography.
• Water will want to flow downwards.
• We can do the same with electric fields.
Electric “Field”
• The Electric Field is just a measure of the
electric topography.
• Since protons repel each other you can think of
the protons as hills.
• The electrons would be pits or valleys.
• The elevation of some point near some charges
would depend on the distribution of charges
(much like your elevation depends on where you
are compared to the hills and valleys).
• Units are in N / C.
Calculating the Electric Field
• First lets do it for just one charge.
• For one charge the equation is pretty
straightforward:
• E = -kq / r2 (towards the charge)
• q is the charge (in Coulombs), k is a
constant (=9*109), and r is the distance
you are away from the charge.
Sample problem
• Suppose q = 5 C and r = 2 m.
• What is the value of E?
2nd sample problem
• What is the electric field at the position of
the charge?
Next step, add in another charge,
but leave it all in 1 dimension
• Now we will have 2 charges. Each is going to
add to our electric field.
• Direction is important!
• The field will just be the sums of the fields from
each charge. Add them up!
• Okay lets try one.
• At X = +2 we have a charge of +5C.
• At X = -3 we have a charge of +9C.
• What is the electric field at X= 0 (remember
direction)?
• (note to self work on next page)
Sum them.
• At X = +2 we have a charge of +5C.
• At X = -3 we have a charge of +9C.
• What is the potential (remember direction).
• E = -kq / r2
• So, for the 1st charge (q1) you have -5*9*109 /4
(N/C)(+x direction)
• For the 2nd (q2) you have –9*9*109 /9 N/C (-x
direction)
• So, your total is -2.25*109 N/C (x direction)
Two dimensions!
• Okay now it gets a bit tricky.
• Here you need to sum vectors.
• And there are a few tricks…
• Here I will give you a refresher on vectors
Key to break down E field vectors
• The proportions of the distances will be
the same as the proportions of the E field.
• That is to say if you were to have a
3(x),4(y),5(hypotenuse) right triangle in
terms of distance from the charge to
where you measure that Ex will be 3/5’s of
E hypotenuse, and Ey will be 4/5’s of E
total
And so
• E hyponenus still = E = -kq / r2 (towards the
charge)
•
•
•
•
Then:
Ex = E hyp * x/r
Ey = E hyp * y/r
Where x and y are the x and y distances from
where you are measuring the field to where the
charge is
• Note x and y can be negative
2D example
•
•
•
•
Charge 1: q = -2C, X = 0, Y = 2
Charge 2: q = 5C, X = 3, Y = 4
Hint 1, find r for charge 2.
Hint 2, find total for charge 2, then the x/y
components.
• The question: find the magnitude of the
electric field at the origin.
Warning
• Since the problem has in the word
“magnitude” the temptation is to throw the
vectors out the window, the window, the
2nd story window
• Only get the magnitude at the very end
Ready for 3 charges?
• Oops, we are out of time. Guess we will
do that in recitation.
Conclusion
• 1) We learned how to find the Electric
Field for 1 charge by using E = -kq / r2
• 2) When there is more than 1 charge, you
just add them up. The only tricky thing is
to do find the E for each charge in vector
form then add them up using geometry.
• Questions?
• Tomorrow: Electric Force.