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Electrostatic potential

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3. (a) Four point charges are placed at the vertices of a square as shown in the diagram.
The charges are of equal magnitude, Q, the sign of each charge is given in this diagram (attached).

(i) What is the value of V x E at all spatial points in this configuration of charges (note that the charges are stationary)? What is the significance of this result?

(ii) What is the electrostatic potential, V, at the following points: (0,0), (0, +a), (+a, 0)?

(iii) How much total work must be done to bring a charge of -2Q from spatial infinity and place it at the origin?

(iv) With this fifth point charge at the origin, how much total work must be done to place a sixth charge of +Q at the point (0, +a)?

(b) A dielectric slab (medium 2) is placed in the plane y = 0 and is surrounded by two other media as shown in
the adjacent diagram. The relative permittivities are (attached).

None of the media contain any free volume or surface charge. In medium 3 there is a uniform electric field.

(i) State the boundary conditions on D and E at the interface between two materials.

(ii) Find the electric field, E2, the electric displacement, D2 and the polarization vector, Pg, in medium 2.

(iii) Find the surface density of bound charge on both sides of the boundary between media 1 and 2, and on both sides of the boundary between media 2 and 3.

(iv) Does the magnitude of the electric field vary from one medium to the next?
If so, in which medium is the magnitude of the electric field the greatest?

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In the following posting, the expert helps solve several problems in electrostatics.

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Electrostatic potential energy & electrical potential

See attached file.

The problems are from Physics 7th edition by Cutnell & Johnson.

1. During a particular thunderstorm, the electric potential difference between a cloud and the ground is Vcloud - Vground = 1.90 108 V, with the cloud being at the higher potential. What is the change in an electron's electric potential energy when the electron moves from the ground to the cloud?

2. Point A is at a potential of +290 V, and point B is at a potential of -150 V. An α-particle is a helium nucleus that contains two protons and two neutrons; the neutrons are electrically neutral. An α-particle starts from rest at A and accelerates toward B. When the α-particle arrives at B, what kinetic energy (in electron volts) does it have?

3. In a television picture tube, electrons strike the screen after being accelerated from rest through a potential difference of 27 000 V. The speeds of the electrons are quite large, and for accurate calculations of the speeds, the effects of special relativity must be taken into account. Ignoring such effects, find the electron speed just before the electron strikes the screen.

4. Point A is located 0.20 m away from a charge of -2.70 10-9 C. Point B is located 0.50 m away from the charge. What is the electric potential difference VB - VA between these two points?

5. An electron and a proton are initially very far apart (effectively an infinite distance apart). They are then brought together to form a hydrogen atom, in which the electron orbits the proton at an average distance of 5.50 10-11 m. What is EPEfinal - EPEinitial, which is the change in the electric potential energy?

6. Location A is 3.30 m to the right of a point charge q. Location B lies on the same line and is 4.20 m to the right of the charge. The potential difference between the two locations is VB - VA = 45.0 V. What is the magnitude and sign of the charge?

7. Two identical point charges are fixed to diagonally opposite corners of a square that is 1.4 m on a side. Each charge is +3.5 µC. How much work is done by the electric force as one of the charges moves to an empty corner?

8. Two charges are fixed in place with a separation d. One charge is positive and has twice (n = 2) the magnitude of the other charge, which is negative. The positive charge lies to the left of the negative charge, as in the figure. Relative to the negative charge, locate the two spots on the line through the charges where the total potential is zero.

positive distance to the left of -q d

positive distance to the right of -q d

9. A charge of -1.5 µC is fixed in place. From a horizontal distance of 0.0675 m, a particle of mass 6.75 10-3 kg and charge -2.8 µC is fired with an initial speed of 25.0 m/s directly toward the fixed charge. How far does the particle travel before its speed is zero?

10. Four identical charges (+2.5 µC each) are brought from infinity and fixed to a straight line. The charges are located 0.55 m apart. Determine the electric potential energy of this group.

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