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The force of the system is .
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- A sphere of radius r has potential Vo sin 20 cos 2 on its surface. Find the scalar potential inside and outside the sphere.What is the potential difference V(r) – V(0) for r < a (i.e., where r is inside the insulating sphere, and V(0) is the potential at the origin)?I. 2) Consider the following potential U= x'-4x. a) Find the equilibrium point/points. b) Find the work done by the force if the particles move from x = 0 to x =4m. c) What is the force applied to the particle at x = 4m.
- Find the electrical potential at point P. 2R R. 3R The electric potential for a ring of radius a at the same point (distance x) is: Select one: O to. 쁜(VI3 + v10) b. 쁜(V5+ v17) C. 쁜(VI3-VT0) O d. 쁜(V5-V17)Consider the potential distribution V = 5r² sin 0 sin ø. Find: Py everywhere i. ii. The energy required to move 2 µc from A(x=3, y-4, z=5) to B(x=6, y=8, z=10)If the potential function (Scalar) is given by V = -3xy'z', then determine the gradient of the potential and gradient at point (1, -1, 1) gaz O-Gy z'a, + 6xyz*a, + 9xy*z*a_), - 3a, + 6a, - 9a, + 9xy²z²a,), -3a, + 6a /2 9az O 3y z'a, + 6xyza, + 9xy*z*a, 3a, - 6a, - 90, + 9xy²z? 30x + 9xy²z²a,), 3a, -(3y²z'a, - 6xyza, + 9xy z²a,), 3a,e - 6a, - 9a, 902 3y²z'a, + 6xyz'a, + 9xy'z2a,, -3a, - 6a, - 9a, 9xy²z²a,, -3a,
- a) What is the general expression of force resulting from the L-J potential? b) At what value of the distance x does the potential have its minimum, if x0 = 0.34 nm? (Hint: how do you find a minimum or a maximum of a function y(x)? How do you make sure it is a minimum?)find a potential function for the given vector field. F(x, y) = 3x 2 cos y, −x3 sin y F(x, y) = e y sec 2 x,e y tan x3. Given the following scalar potentials (V), calculate the solution for the gradient of V (VV), and plot the vector arrow representation of this vector field over the given limits. (a) V = 15 + r cos o, for 0 < r < 10, and 0 < $ < 2n. (b) V = 100 + xy, for –10 < x < 10,
- The electric potential is given by V(r.y.) = Ar'y's where A is a costant. Find the electric potential (where i, j, and k are the unit vectors correnponding to a, , al: Aes in the three dimensioual Carteniau Coordinate System). Select one: O -Ar'y:(i + j + k) O -Ar'y:(3i + 2j + k) 3Ayai + 2Arysj+ Ary7kConsider the electric potential (x, y, 2) = Vo a(1/m) - ry(V/m2)+ ay:(V/m) It is given that the electric field vanishes at point P with coordinates (a, y, 2) = (0, -1, -1) m. Find the constant V, in Volts.The electric field of a charge distribution is found to be E = f Eoe +). where Eo, µ are constant parameters and r is the radial distance to the origin of the coordinate system, which also coincides with the radial coordinate. r is the unit vector along the direction of increasing r. What is the corresponding electric potential at coordinate r, if the potential goes to zero as r o? Select one: V(r) = Eo, e ur V(r) = Eo e kr V (r) = E o V(r) = Eo