worksheet13

# worksheet13 - 6 C at (1,0), with the distances measured in...

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# Worksheet 13 - 2006 Due Thursday 20th April 9pm This worksheet gives you some more practice at problem solving using mathematica. PROBLEM 1. Make a 3-d plot of the function Sin ( xy ) for [0 , 3] and [0 , 3]. PROBLEM 2. Numerically Fnd the roots to the equation x 6 - 4 x 2 = 2. How many are real and how many are imaginary? PROBLEM 3. Solve the following equation analytically using mathematica d 2 x/dt 2 + 5 x = 1 . 5 sin (2 t ), with the initial conditions x (0) = 1 , x 0 (0) = 0. Plot the resulting solution. Give an example of a physical system which leads to this equation. In the system you have chosen what are the units of the numbers 5,1.5 and 2 appearing in the equation. PROBLEM 4. ±our point charges are placed at the corners of a square, with q 1 = 10 - 6 C at (0,1), q 2 = - 2 × 10 - 6 C at (1,1), q 3 = - 3 × 10 - 6 C at (0,0) and q 4 = 2 × 10 -
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Unformatted text preview: 6 C at (1,0), with the distances measured in centimeters.- a) ind an expression for the electrostatic potential, V , at arbitrary position (x,y). Note that the contribution of each charge to the total elec-trostatic potential is simply Kq/r. It is a scalar. The total electrostatic potential at any point is a sum of the electrostatic potentials for each of the point charges lying on the square). Make a 3-d plot of this potential on the interval (0.05,0.95).- b) ind the vector force on a charge q = 1 10-6 C placed at position (2,1). Note that the force is related to the electric Feld via ~ F = q ~ E . The electric Feld is related to the electrostatic potential by ~ E =-~ V . 1...
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## This note was uploaded on 07/25/2008 for the course PHY 102 taught by Professor Duxbury during the Spring '08 term at Michigan State University.

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