Given the nonuniform field E = yäz + xãy + 2ã, determine the work expended in carrying 2C from B(1,0,1) to A(0.8,0.6,1) along the shorter arc of the circle x2 + y2 = 1,z = 1.
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- Calculate the angular velocity ω of an electron orbiting a proton in an atom, assuming the radius of the orbit is 5.02×10^-11 m. You may assume that the proton is stationary and the centripetal force is supplied by Coulomb attraction.Four equal charges, q, are fixed at the corners of a square of side a in the xy-plane centered on the origin. A bead of mass m and charge -q is positioned at the origin. A thin, frictionless string along the z-axis threads the bead, thus restricting its mo- tion to the z-axis. The bead is then displaced from the origin by a small amount Zo < 0 and released from rest. Show that the bead undergoes simple harmonic motion (to a very good approximation), and derive an expression for its period of oscillation in terms of known parameters.A dipole with –Q at the origin (0,0) and the +Q at coordinates x= 4.00 cm, y = 3.00 cm is in an Electric field, E = 4.25 V/m directed to the right, +x . (Q = 0.400 C) Find the dipole moment.
- We will do the following processes:a) First we take three point particles of mass (m1, m2, m3) from infinity and glue them to positions (x1, x2, x3) relative to some global inertial reference system.b) We now carry three positively charged particles qi, i ∈ (1, 2, 3) from infinity and glue them to positions (y1, y2, y3) relative to some global inertial reference system.Explain of these two processes if the external world gained or lost energy?Evaluate the energy gained or lost from the outside world. Is there conservation of energy in these processes?An isolated water molecule is modeled as two point charges ±0.700e separated by 0.0980 nm. Its rotational inertia is 2.93 × 10−47 kg·m2 about the axis shown in the figure below. The molecule is in a uniform electric field of magnitude 838 N/C. If the molecule is initially at rest at θ = 90.0°, what is its angular speed when it reaches θ = 0, assuming no other forces or torques? rad/s