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 * 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 / r 2 (towards the charge) q is the charge (in Coulombs), k is a constant (=9*10 9 ), 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?

2 nd 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 / r 2 So, for the 1st charge (q1) you have -5*9*10 9 /4 (N/C)(+x direction) For the 2 nd (q2) you have –9*9*10 9 /9 N/C (-x direction) So, your total is -2.25*10 9 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 / r 2 (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 2 nd 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 / r 2 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.