A long cylinder of radius 2 cm carries a charge of 5 µC / m2 kept in a medium of dielectric constant 50. Find the electric field intensity at a point situated at a distance 1 m from the axis of cylinder.
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- A dielectric rod with cross-section area of A and polarization of Px = ax² + b is extended from x = 0 to x = L. (a) Calculate the bound volume charge density and bound surface charge density. b) Determine the total bound charge.Wanda has shrunk Timmy down to a very small size so that he can study for his science test. He observes a charge of -4.255x10^-6C. that starts at rest in a region of constant, uniform electric field. Assume gravitational effects are negligible. At a time of 12.45s after the charge starts from rest, Wanda measures that the charge has a kinetic energy of 2.996x10^-6J. What would be the potential difference, in volts, the charge will move through after 8.310s?A charged conducting sphere with capacitance, C = 26.7 pF, produces an electric field that points radially outward. At a distance, d = 61.2 cm, from the center of the sphere, the strength of the electric field is E = 71.3 kV/m. (a) What is the radius of the charged sphere? R = m (b) Find the sphere's surface charge density. μC/m² J =
- The membrane surrounding a living cell consists of an inner and an outer wall that are separated by a small space. Assumne that the membrane acts like a parallel plate capacitor in which the effective charge density on the inner and outer walls has a magnitude of 7.1x 10-6 C/m2.(a) What is the magnitude of the electric field within the cell membrane? (b) Find the magnitude of the electric force that would be exerted on a potassium ion (K*; charge = +e) placed inside the membrane. (a) Number Units (b) Number UnitsLiquid water has a large dielectric constant of ɛ, = 80. Suppose that a single sodium ion (Na+, carrying a positive charge of +1e) is held in the middle of a beaker of pure water. Compared to the volume of the sodium ion, the volume of the water can be effectively treated as infinite. a) Write down the electric displacement at r distance away from the sodium ion. b) Write down the electric field at r distance away from the sodium ion. c) Write down the electrostatic force that the sodium ion acts on a water molecule that is 2nm away from the ion and oriented with its dipole moment radially away from the ion. d) Calculate the polarization at a distance r = 2nm away from the sodium ion. e) The dipole moment of a water molecule is 6.17 x 10-30C · m. Estimate how much fraction of the water molecules that are at 2nm away from the sodium ion are reoriented by the sodium ion. (Assume that there are only two possible states for these water molecules: either randomly oriented and showing zero…An isolated charged conducting sphere has a radius R = 13.0 cm. At a distance of r = 24.0 cm from the center of the sphere the electric field due to the sphere has a magnitude of E = 4.90 × 104 N/C. (a) What is its surface charge density (in µC/m²)? μC/m² (b) What is its capacitance (in pF)? pF (c) What If? A larger sphere of radius 26.0 cm is now added so as to be concentric with the first sphere. What is the capacitance (in pF) of the two-sphere system? pF
- Two pieces of tape are stuck together, and then ripped apart, forming an electric dipole with one piece of tape at +0.20nC, the other at -0.20nC, held 3.0cm apart from each other. What is the electric field at a point positioned 10.0cm from the positive charge and 13.0cm from the negative? If a capacitor has an electric field with a magnitude of 1 microNewton/Coulomb exactly halfway between its positive and negative plates, which are each one square meter, then how much charge is on its positive plate? please provide correct significant figures in answer.Two pieces of tape are stuck together, and then ripped apart, forming an electric dipole with one piece of tape at +0.20nC, the other at -0.20nC, held 3.0cm apart from each other. What is the electric field at a point positioned 10.0cm from the positive charge and 13.0cm from the negative? If a capacitor has an electric field with a magnitude of 1 microNewton/Coulomb exactly halfway between its positive and negative plates, which are each one square meter, then how much charge is on its positive plate? please provide correct significant figures in answer.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/s²
- The membrane surrounding a living cell consists of an inner and an outer wall that are separated by a small space. Assume that the membrane acts like a parallel plate capacitor in which the effective charge density on the inner and outer walls has a magnitude of 6.8 × 10-6 C/m2. (a) What is the magnitude of the electric field within the cell membrane? (b) Find the magnitude of the electric force that would be exerted on a potassium ion (K+; charge = +e) placed inside the membrane.parallel-plate capacitors are widely used in electronics such as preventing direct current leakage. An electric field is generated between a pair of plates that has a surface charge density of 7.70 x 10^-6 C/m^2 The plates are seperated by 0.49 um. a) what is the magnitude of the electric field between the plates ? b) suppose the thickness of the plates doubled, would my answer increase, decrease, or remain the same?The electric field 1⁄4 of the distance from qA to qB has a magnitude of zero. What must be true about qA and qB?