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Goal: To understand what Electric Fields are and how to calculate them.

Goal: To understand what Electric Fields are and how to calculate them. Objectives: Understanding what charges are. Knowing how to produce a charge. How to calculate an electric field from a collection of charges. What is charge?.

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Goal: To understand what Electric Fields are and how to calculate them.

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  1. Goal: To understand what Electric Fields are and how to calculate them. Objectives: Understanding what charges are. Knowing how to produce a charge. How to calculate an electric field from a collection of charges

  2. 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.

  3. 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)

  4. Electric Field • Suppose you wanted to know where the water would flow when it rains. • How would you do that?

  5. 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.

  6. 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.

  7. 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.

  8. Sample problem • Suppose q = 5 C and r = 2 m. • What is the value of E?

  9. 2nd sample problem • What is the electric field at the position of the charge?

  10. 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)

  11. 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)

  12. 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

  13. 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

  14. 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

  15. 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.

  16. 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

  17. Ready for 3 charges? • Oops, we are out of time. Guess we will do that in recitation.

  18. 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.

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