Mathematically, the period of a pendulum for small angles is expressed by the equation below. T = 2n, To solve for g in the equation above, the correct rearrangement of the formula is T. A. g= %3D 4T L В. g %3D C. g 2n1 %3D T2L D. g = %3D

How close together should two electrons get so that their electric potential energy would be 1 Joule?

Show that the vector field is conservative

Two charges Q₁ = 6.2μC and Q2 = 5.9μC are placed on the two corners of a rectangle with the sides a = 6.9mm and b = 14.3mm as shown in the figure below. How much work is required to 5.3mm away from = bring a thir charge Q3 = 5.1μC from infinity to point P that is a distance c Q₁? Please take k J or N.m. Q₁ a - 9.0 x 10°N. m²/C² and express your answer using one decimal place in units of b P Q2 0.2

8. Compute the work done by the force field F(x, y, z) = x²zi- yx²j+ 3xzk acting on an object moving along the straight line from point (1, 1, 0) to (1, 1, 1) to (0, 0, 0).

6. Consider the action S=FFd²x. Vary the potential according to A → A+μ where is a scalar field. Determine the variation in the action.

Please explain why.

Please explain why.

In an electron microscope, there is an electron gun that contains two charged metallic plates 3.15 cm apart, An electric force accelerates each electron in the beam from rest to 9.40% of the speed of light over this distance. (Ignore the effects of relativity in your calculations.) (à) Determine the kinetic energy of the electron as it leaves the electron gun. Electrons carry this energy to a phosphorescent viewing screen where the microscope's image is formed, making it glow. (b) For an electron passing between the plates in the electron gun, determine the magnitude of the constant electric force acting on the electron. N (c) Determine the acceleration of the electron. m/s2 (d) Determine the time interval the electron spends between the plates.

Three charged particles of q₁ = 30.0 nC, q₂ = -30.0 nC, and q3 = 15.0 nC are placed on the y-axis, as shown in the figure. 9₁ 9₁ 9₁ x Charge q₁ has the coordinates (0, 8.00 cm), 9₂ has the coordinates (0, -8.00 cm), and q3 is located at the origin. (a) Find the electric potential energy (in J) of the configuration of the three fixed charges. (b) A fourth particle, with a mass of 1.98 x 10-13 kg and a charge of 94 = 60.0 nC, is released from rest at the point (6.00 cm, 0). Find its speed (in m/s) after it has moved freely to a very large distance away. m/s