The amount of work you have to do to move a charge q from point Pi to point P2 through a small displacement Ar in the presence of an electric field E is given by: P is the angle between the direction AW=F · Ar = - qE·Ar = q |E| |Ar| coso. you exert of the electric field and the direction of displacement Ar. This tells us that the work is dependent on: the magnitude and type (+ or -) of the electric charge we are trying to move, the strength of the electric field we are moving it through, the displacement (change in position from starting point to ending point), and the angle the displacement makes with the electric field. 1) If the angle the displacement makes with the electric field is 90° it means the charge is moving across (or perpendicular to) the field vectors. Is work being done and what is doing the work? Will it be Maximum, Minimum or zero? Explain your answer with a diagram.

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ww Find the work done to transfer a point charge q=+5 µC in the electric field: wwwwwww Ē=yî-xj From point P1(1, 2,-4)m to point P2(-2, 8,-4)m Along the parabola: a) -40 μJ b) +40 µJ y=2x². c) -30 μJ d) +30 µJ e) -20 μJ

An electric dipole is made of two charges of equal magnitudes and opposite signs. The positive charge, q=1.0 μC, is located at the point (x, y, z) = (0.00 cm, 1.0 cm, 0.00 cm), while the negative charge is located at the point (x, y, z) = (0.00 cm, −1.0 cm, 0.00 cm). How much work will be done by an electric field =3.0×106 N/C) to bring the dipole to its stable equilibrium position?

= Two point particles have equal charge q 1100 esu and different masses, m₁ = 25 gr and m₂ = 65 gr, are confined to move freely along the x axis. Note that esu is the unit of electric charge when working with units of mass in grams and distance in centimeters. = The electrical force between the particles is a repelling force which is derived from the potential energy function U(x1, x2) of the two-particles system. U(x1, x2) depends only on the distance of the particles and is given by U(x1, x2) - q2 | x2 − x1| At t = 0) the particle of mass m2 is at rest at the origin (x2 = 0), and the particle of mass m₁ begins to move from point x1 = 76 cm with velocity vo 134 cm/s towards particle m2. = a. What is the location of the center of mass (in cm) at t - 0? -21. b. What is the location of the center of mass (in cm) at t = 0.4 sec? -6.2 c. What will be the minimum distance (in cm) between the two particles? 6.46 X d. Once the distance between the particles is minimal, what will be the speed…

+Q +Q ves Bombes K +Q Q: +Q ta -a O a +29 A positive point charge +Q is located at x = -a. What is the electric potential energy of the system after an external agent bring in a second equal positive charge +Q from infinity to x = +a? (b) With the two equal point charges at x = -a and x = +a, what is the total electric potential energy of the system when an external agent brings in a third charge -Q from infinity to the origin? (c) By how much does the electric potential energy change when the charge -Q is moved from the origin to the point x = +2a along the semicircular path shown? Hint: how is the electric potential energy related to the electric potential?

The figure below shows a small, charged sphere, with a charge of q = +38.0 nC, that moves a distance of d = 0.171 m from point Ato point B in the presence of a uniform electric field E of magnitude 280 N/C, pointing right.   (a) What is the magnitude (in N) and direction of the electric force on the sphere? magnitude n?   (b) What is the work (in J) done on the sphere by the electric force as it moves from A to B?   J??   (C) What is the change of the electric potential energy (in J) as the sphere moves from A to B? (The system consists of the sphere and all its surroundings.)   PEB − PEA =  ?  J   (D)What is the potential difference (in V) between A and B? VB − VA = ? V

O West -1.36 x 10-3 J zero South A charge of 42.0 nC is placed in a uniform electric field that is directed towards the west direction and has a magnitude of 5.40 x 104 V/m. What work is done by the electric force when the charge moves a distance of 1.50 m in the direction 53° south of west? North -2.05 x 10-3 J 3.40 x 10-3 J East

The figure below shows a charged particle, with a charge of q = +39.0 nC, that moves a distance of d = 0.162 m from point A to point B in the presence of a uniform electric field E of magnitude 255 N/C, pointing right. B + (a) What is the magnitude (in N) and direction of the electric force on the particle? magnitude direction Select--- (b) What is the work (in J) done on the particle by the electric force as it moves from A to B? (c) What is the change of the electric potential energy (in J) as the particle moves from A to B? (The system consists of the particle and all its surroundings.) PEB - PEA = (d) What is the potential difference (in V) between A and B?