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A different review A review of the following topics by working on problems 1.Electric charge, potential, force, field and flux. Coulomb's Law Gauss’s Law.

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Presentation on theme: "A different review A review of the following topics by working on problems 1.Electric charge, potential, force, field and flux. Coulomb's Law Gauss’s Law."— Presentation transcript:

1 A different review A review of the following topics by working on problems 1.Electric charge, potential, force, field and flux. Coulomb's Law Gauss’s Law. 2.Capacitance and resistance. Ohm’s Law. 3.Circuits. Kirchhoff’s Rules.

2 Electric field of a dipole Calculate the electric field of a point on the x and y axis, far away from an electric dipole. x x P Formula to use: For a point on x:

3 Calculate the electric field of a point on the x and y axis, far away from an electric dipole. x x P For a point on y, the field y components cancel.

4 Electric field of a charged rod Calculate the electric field at the origin O of the coordinator system, generated by an evenly charged rod with total charge +Q, with length l, and placed distance a away from O on the x-axis. O Formula to use: Because all the charge is concentrated on the x-axis, the electric field has only the x component, pointing to negative x direction at point O. Choose a small section on the rod: The electric field at point O:

5 Force/field equilibrium Two small positively charged beads are fixed at the ends of a horizontal insulating rod. A third small charged bead is free to slide on the rod. At what position is the third bead in equilibrium? Is this a stable equilibrium? Formula to use: Condition for equation: equilibrium on the third bead. Special case: 1-D problem. Construct the x-coordinate system. O x Construct equation: q3q3 solution:discard: (Why?)

6 stable equilibrium ? Translate: prove that the electric potential energy of the whole system when bead 3 at position x is the minimum. O x q3q3 Change bead 3 by, the change in potential energy is Formula to use: Answer: bead 3 at stable equilibrium.

7 Gauss’s Law a type X problem? A sphere of radius 2 a is made of insulating material that has uniform volume charge density ρ. Assume that the material itself does not affect the electric field (i.e., ignore its dielectric effect). A spherical cavity of radius a is made in the original sphere as shown in the figure. Calculate the electric field in the cavity. It is a Gauss’s Law problem. Put the material back to the cavity, the problem is type I. The electric field inside the sphere is: See example in lecture note

8 Now the electric field of the material of the cavity:

9 Some easier problems Finding the C eq But So Solve the is equation, we get

10 Some easier problems Finding the C eq Wire has no resistance. Re-draw the diagram: 4.0 μF 6.0 μF 5.0 μF 7.0 μF a b So

11 Kirchhoff’s rules Determine the current in each branch. L1 L2 I1I1 I3I3 I2I2 Step 1: choose and mark the loop. Step 2: choose and mark current directions. Mark the potential change on resistors. Step 3: apply junction rule: Step 4: apply loop rule: Step 5: simplify and solve the three equations for the three variables. + – – – – + + + – +


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