Two point charges q are placed at the positions ⃗r1 = Lxˆ and ⃗r2 = −Lxˆ. Find the potential and electric field on the z axis.
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Two point charges q are placed at the positions ⃗r1 = Lxˆ and ⃗r2 = −Lxˆ.
Find the potential and electric field on the z axis.
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- Opgave 25.32: (a) A sheet with charge Q uniformly distributed over its area A is surrounded by a dielectric. Show that the sheet creates a uniform electric field at nearby points and derive an expression for the magnitude of the field. (b) Two large sheets of area A, carrying opposite charges of equal magnitude Q, are a small distance d apart. Show that they create a uniform electric field in the space between them and derive an expression for the magnitude of the field. (c) Assume the negative plate is at zero potential. Derive an expression for the potential at the positive plate. (d) Derive an expression for the capacitance of the pair of plates.A parallel plate capacitor has a surface charge density of magnitude o = 0.00433 C/m² on each plate. A small sphere, charged to Q = 9.40 × 10-6 C and located between the plates, undergoes a displacement of magnitude d = 0.143 m. Refer to the figure, which is not drawn to scale. y +++++++ Using the symbols in the palette, not their numeric equivalents, enter an expression, in Cartesian unit-vector notation, for the electric field within the capacitor. If the displacement is from left to right, then how much work, in joules, is performed on the sphere by the electric field? At what speed, in meters per second, is the sphere moving when it completes the displacement if it starts from rest and its mass is 0.115 kg? XA particle of charge q is fixed at point P, and a second particle of mass m and the same charge q is initially held a distance r1 from P. The second particle is then released. Determine its speed when it is a distance r2 from P. Let q = 2.8 µC, m = 30 mg, r1 = 1.3 mm, and r2 = 2.6 mm.
- A charge Q1 = 1.33 μC is at rest and is located 2.30 cm away from another fixed charge Q2 = 1.85 μC. The first charge is then released. Calculate the kinetic energy of charge Q1 when it is 5.00 cm away from charge Q2.An electron and a proton are fixed at a separation distance of 859 nm. Find the magnitude E and the direction of the electric field at their midpoint. The direction E = N/CA particle (charge = 6.1 μC) is released from rest at a point x = 19.3 cm. If a 78.1-μC charge is held fixed at the origin, what is the kinetic energy of the particle after it has moved 98.2 cm?
- A ring and a disk both are centered at (0, 6, 3) and are both lying on the plane y = 6. The ring has a radius of 7 m, while the disk has a radius of 9 m, so that the ring is around the disk. Determine the magnitude of the electric field in kV/m at point (0, -9, 3) if the ring has a total charge of -8 mC and the disk has a total charge of 6 mC. All coordinates are measured in meters.Two red blood cells each have a mass of 5.05 × 10-¹4 kg and carry a negative charge spread uniformly over their surfaces. The repulsion arising from the excess charge prevents the cells from clumping together. Once cell carries -2.60 pC of charge and the other -2.70 pC, and each cell can be modeled as a sphere 8.20 µm in diameter. What minimum relative speed u would the red blood cells need when very far away from each other to get close enough to just touch? Ignore viscous drag from the surrounding liquid. V = What is the magnitude of the maximum acceleration amax of each cell? Cmax = m/s m/s²A particle (charge = 3 µC) is released from rest at a point x %3D = 11.4 cm. If a 61.1-µC charge is held fixed at the origin, what is the kinetic energy of the particle after it has moved 94.1 cm? Round your answer to 2 decimal places.
- A positively charged particle of mass 50 grams and charge 10 µC is released from rest at the origin in the uniform electric field of 100 N/C directed along the +X-axis. Determine its speed at x = 10 cm position.The drawing shows an electron entering the lower left side of a parallel plate capacitor and exiting at the upper right side. The initial speed of the electron is 3.13 × 106 m/s. The capacitor is 2.00 cm long, and its plates are separated by 0.150 cm. Assume that the electric field between the plates is uniform everywhere and find its magnitude. 15.30 + A + 2.00 cm Number i + + + 0.150 cm UnitsA parallel plate capacitor consists of two rectangular, horizontally oriented plates, each with an area of 4.00 cm2, and separated by a distance of 0.300 mm. If the magnitude of the charge on each capacitor is 5.00 nC, what is the magnitude of the electric field between both plates?