A metal object having a length (10m), cross section area (0.5 mm2), and resistance (0.5N) is connected to a potential difference source of 5V at room temperature. If the density of free electrons equals (8×1025 electron/m³), Calculate the current through the object.
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- Problem 6: The voltage across a membrane forming a cell wall is 83 mV and the membrane is 9.25 nm thick. What is the electric field strength in the cell wall, in volts per meter? E = sin() cotan() atan() acotan() cosh() tanh() cos() asin() O Degrees tan() π ( ) 789 acos() E ^^^ 4 5 6 sinh() 1 1 2 3 cotanh() + 0 Radians VOBACKSPACE HOME END DEL CLEARA metal object having a length (10m), cross section area (0.5 mm2), and resistance (0.52) is connected to a potential difference source of 5V at room temperature. If the density of free electrons equals (8×1025 electron/m³), Calculate the thermal velocity.Volume charge density within the operating region of a parallel-plate vacuum diode is given by p = -(%)e, Vo d-41³x-2/3, where the cathode is located at x = 0 and the anode at x = d. The voltage between anode and cathode is Vo. If Vo = 40 V and d = 1 cm, find the total charge in a 1-m? cross section lying between: (a) x = 0 and x = d/2; (b) x = d/2 and x = d. %3D
- An electron is fired at a speed vi = 4.1 × 106 m/s and at an angle θi = 38.2° between two parallel conducting plates as shown in the figure. If s = 1.9 mm and the voltage difference between the plates is ΔV = 98.3 V, determine how close, w, the electron will get to the bottom plate. Put your answer in meters and include at 6 decimal places in your answer.If a capacitor consisting of parallel plates with dimensions w and l, gap g, permeability ε and if the voltage of the plates is V, then the electrostatic energy isParticle of mass 9x10-31 kg and a negative charge of 1.6x10-19 C is projected horizontally with a velocity of 106 ms into a region between two infinite horizontal parallel plates of metal. The distance between the plates is d 0.3 cm and the particle enters 0.1 cm below the top plate. The top and bottom plates are connected, respectively, to the positive and negative terminals of a 30 V ballery. Find the components of the velocity of the particle just before it hits one of the plates. = y + e + + VO Fig. % E + +
- Suppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius rg has a charge of +Q, while the outer cylinder of radius r, has charge -Q. The electric field E at a radial distance r from the central axis is given by the function: E = ae-T/ao + B/r + bo where alpha (a), beta (8), ao and bo are constants. Find an expression for its capacitance. First, let us derive the potential difference Vab between the two conductors. The potential difference is related to the electric field by: Voh = Ed Edr Calculating the antiderivative or indefinite integral, Vab = (-aaoe-r/a0 + B + bo By definition, the capacitance Cis related to the charge and potential difference by: C = Evaluating with the upper and lower limits of integration for Vab, then simplifying: C = Q/( (erb/ao - eralao) + ß In( ) + bo ( ))Particle of mass 9x10-31 kg and a negative charge of 1.6x10-19 C is projected horizontally with a velocity of 106 ms into a region between two infinite horizontal parallel plates of metal. The distance between the plates is d = = 0.3 cm and the particle enters 0.1 cm below the top plate. The top and bottom plates are connected, respectively, to the positive and negative terminals of a 30 V ballery. Find the components of the velocity of the particle just before it hits one of the plates. y |+ + ~ る VO Fig. + t + + Vx Vy Pom E dElectrons in silicon have a mobility of 1000 cm /V-sec. The electric field is applied to make the electrons reach a velocity of 3 x 10' cm/sec. Assume that the mobility is constant and independent of the electric field. What voltage is required to obtain this field in a 5 um thick region? How much time do the electrons need to cross the 5 um thick region?
- Particle of mass 9×10-31 kg and a negative charge of 1.6x10-19 C is projected horizontally with a velocity of 106 ms into a region between two infinite horizontal parallel plates of metal. The distance between the plates is d 0.3 cm and the particle enters 0.1 cm below the top plate. The top and bottom plates are connected, respectively, to the positive and negative terminals of a 30 V ballery. Find the components of the velocity of the particle just before it hits one of the plates. y |} 2 + + Vo Fig. " E + +Three point charges Q1 = 1 mC, Q2 = -2mC, and Q3 = 3 mC are, respectively, located at (0, 0, 4), (-2, 5, 1), and (3, - 4,6). Prompts Submitted Answers Find the potential Vp at P(-1, 1, 2). Choose a match Calculate the potential difference V Po if Q is (1, 2, 3). Choose a match2 / 2 150% 4. A potential difference V, is applied, with a battery, to the plates of a parallel-plate capacitor of plate-area A and separation d. Write an expression for each of the following (a) the capacitance C, of the capacitor, (b) the free charge qo, (c) the electric field strength E, in the gap. Now the battery is disconnected and a dieleetric slab of thickness b and dielectric constant k is inserted in the gap. (d) What happens to the free charge? (c) What happens to the field strength in the gap? () What is the field strength in the dielectric slab? (g) Find an expression for the potential difference between the two plates. (h) Find an expression for the capacitance C now. (i) Assume that C becomes double of C, when a slab of dielectric constant 10 is nserted. What is the thickness b? Ai