A uniform electric field of magnitude 260 V/m is directed in the positive x direction. A +15.0 μC charge moves from the origin to the point (x, y) = (20.0 cm, 50.0 cm). (a) What is the change in the potential energy of the charge field system? ] (b) Through what potential difference does the charge move? v

Three charged particles are at the corners of an equilateral triangle as shown in the figure below. (Let q 7.00 με 60.0° L = 2.00 μc, and L = 0.650 m.) q -4.00 μC x (a) Calculate the electric field at the position of charge q due to the 7.00-μC and -4.00-μC charges. KN/CI + KN/C ĵ (b) Use your answer to part (a) to determine the force on charge q. mNI + mN ĵ

Two point charges are on the y axis. A 4.90-µC charge is located at y = 1.25 cm, and a -2.04-µC charge is located at y = −1.80 cm. (a) Find the total electric potential at the origin. V(b) Find the total electric potential at the point whose coordinates are (1.50 cm, 0).

RC-2 A half ring of charge lies in the x-z plane with its center at the origin as shown to the right. There are λ coulombs per meter of charge evenly distributed along the ring, which has radius 'a'. a) Sketch on your paper figures like the figures shown to the right. On your figures show an arrow representing the electric field at the point P that is produced by source charge element dq. b) Use Coulomb's law to calculate the magnitude of the x, y and z components of the total electric field at P due to the half ring of charge. If any component is equal to zero, you may use the symmetry argument to explain why it is zero instead of doing the calculations. 3D view: ZI (C/m) X dq b View looking from point P toward the origin: Z dq 0

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Three charged particles are at the corners of an equilateral triangle as shown in the figure below. (Let q = 2.00 μc, and L = 7.00 με 60.0° L 0.650 m.) q -4.00 μC x (a) Calculate the electric field at the position of charge q due to the 7.00-μC and -4.00-μC charges. -10636.7 Once you calculate the magnitude of the field contribution from each charge you need to add these as vectors. KN/CI + 128963 Think carefully about the direction of the field due to the 7.00-μC charge. KN/C ĵ (b) Use your answer to part (a) to determine the force on charge q. -21.3 If you know the electric field at a particular point, how do you find the force that acts on a charge at that point? mN I + 257.9 Check units carefully. Note that the field in part (a) is given in KN/J and the force in this part is given in mN. mN ĵ ×

In the figure below, a long circular pipe with outside radius R = 2.38 cm carries a (uniformly distributed) current i- 9.86 mA into the page. A wire runs parallel to the pipe at a distance of 3.00R from center to center. Find the (a) magnitude and (b) direction (into or out of the page) of the current in the wire such that the ratio of the magnitude of the net magnetic field at point P to the magnitude of the net magnetic field at the center of the pipe is 2.48, but it has the opposite direction. (a) Number Units (b) Wire O O Pipe

RC-2 A half ring of charge lies in the x-z plane with its center at the origin as shown to the right. There are λ coulombs per meter of charge evenly distributed along the ring, which has radius 'a'. a) Sketch on your paper figures like the figures shown to the right. On your figures show an arrow representing the electric field at the point P that is produced by source charge element dq. I TI Cul 3D view: zl (C/m) X a b View looking from point P toward the origin: y

2. The 2.50 µC point charges are located on the x-axis. One is at x = 1.00 m, and the other is at x= -1.00 m. (a) Determine the electric field on the y-axis at y = 0.500 m. (c) Calculate the electric force on a -3.50 µC charge placed on the y-axis at y = 0.500 m.

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