6.4. Which one of the following equations is dimensionally homogenous? Show your proof. a. F= ma b. F =m R F(t, -1,) = m(V, – v) F = mV C. d. (V, -V) (f, – 4.) F =m-V) = m- where F= force (N) m = mass (kg) a= acceleration (m's) V=velocity (m's) R=radius (m) 1= time (s)
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- Which of the following is not considered for the formation of Lagrangian function solution? a. Equality Constraint b. Cost function c. Objective Function d. Inequality ConstraintFind the Electric Field at P(6, - 3, - 4) due to: Q_{1} = - 30mu*C at (2, 3, -6)Compute for the potential at A(5, 0, -1) if the potential at the origin is -5 MV in a region in vacuum where the electric field is produced by a 15-mC point charge on (-2, 4, 3). All coordinates are measured in meters. a.) -15.0689 MV b.) -20.6705 MV c.) -10.0689 MV d.) -5.6705 MV
- An infinitely large flat surface has a surface density of electric charge. The surface moves with constant velocity in a parallel direction. Show that the differential version of the Poynting theorem holds at all points above and below the surface.A cylindrical capacitor is made of two concentric conducting cylinders. The inner cylinder has radius R1 = 19 cm and carries a uniform charge per unit length of λ = 30 μC/m. The outer cylinder has radius R2 = 25 cm and carries an equal but opposite charge distribution as the inner cylinder. a. Use Gauss’ Law to write an equation for the electric field at a distance R1 < r < R2 from the center of the cylinders. Write your answer in terms of λ, r, and e0. E= b. Write an equation for the energy density due to the electric field between the cylinders in terms of λ, r, and e0. u = c. Consider a thin cylindrical shell of thickness dr and radius R1 < r < R2 that is concentric with the cylindrical capacitor. Write an equation for the total energy per unit length contained in the shell in terms of λ, r, dr, and ε0. dU/l = d. Calculate the energy stored per unit length in the capacitor in units of joules per meter. U/l = e. Calculate the electric potential difference between…i.A soccer goal, found is a city park, is made up of tubing that supports an odd-shaped hanging net behind the goal, but has a rectangular opening in front. The height of the opening is 2.5m and the width is 3.2m. If a uniform E-field, with a magnitude of 0.1N/C, passes through the goal from the front to the back, entering at 90 degrees to the plane of the goal opening, what is the flux through the net? Also, find the flux through the net if the E-field enters the goal at 60 degrees angle to the plane of the front goal. In both cases, assume that there no charge found inside the goal itself ii.Explain why the electric field intensity, E is zero inside a conductor under static conditions.
- Two coaxial conducting cylinders are located at ρ = 2 cm and ρ = 4 cm in free space and have a length of 100 m. The region between the cylinders contains a layer of dielectric from ρ = 2 cm to ρ = 3.69 cm with εr = 2. The capacitance in nF is?It is a problem from Linear Systems Theory , chapter 2, Linearization i wanna detailed process for solving this problem. line by lineFind the relative permittivity of the dielectric material present in a parallel-platecapacitor if: (a) S = 0.12 m/, d = 80 μm, V = 12 volt, and the capacitor contains1 ?? of energy; (b)The stored energy density is 100 ?/?/, V = 200 volt, and ? =45 ??; (c) ? = 200 ??/? and ?# = 20 ??/?/.
- Hodgkin-Huxley type models represent the biophysical characteristic of cell membranes. The typical Hodgkin-Huxley model treats each component of an excitable cell as an electrical ele- ment, as shown in the figure. Extracellular medium gn(t,v) 60 w Intracellular medium (i) Explain the biological meanings of the capacitance (Cm), conductances (gn and gl), and batteries (E). (ii) State the equations for the current flowing through the lipid bilayer, and the current through a given ion channel. (iii) State the equation for the total current through the membrane of a cell with sodium and potassium channels. Explain the biophysical meaning of all parameters. (iv) Ion pumps and exchangers are represented in the model by current sources (Ip). Explain how the sodium-potassium exchanger functions.This is a two-dimensional problem. Consider a square on the xy plane with vertices at (0,0), (a, 0), (a, a), (0, a). There is no charge or matter inside the square. The sides perpendicular to the x-axis have a potential equal to zero. The side at y = a has a constant potential φ(0), while the one at y = 0 has a constant potential at -φ. Find φ (x, y) for all points within the square.finnd the Electric Field at P (6, -3, -4) due to: Q_{1} = - 30mu*C at (2, 3, -6)