A line of charge starts at x = +x0 and extends to positive infinity. The linear charge density is λ = λ0x0/x, where λ0 is a constant. Determine the electric field at the origin.
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A line of charge starts at x = +x0 and extends to positive infinity. The linear charge density is λ = λ0x0/x, where λ0 is a constant. Determine the electric field at the origin.
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- A line of charge starts at x = a and extends to x = 2a. The linear charge density is λ = b/x3 where b is a constant. Determine the electric field at the origin.A line of charge starts at x=+x0 and extends to positive infinity. The linear charge density is λ=λ 0 x0 /x,where λ 0 is a constant. Determine the electric field at the origin.Positive charge is distributed in a sphere of radius R that is centered at the origin. Inside the sphere, the electric field is Ē(r) = kr-1/4 f, where k is a positive constant. There is no charge outside the sphere. a) How is the charge distributed inside the sphere? In particular, find an equation for the charge density, p. b) Determine the electric field, E(r), for r > R (outside the sphere). c) What is the potential difference between the center of the sphere (r = 0) and the surface of the sphere (r = R)? d) What is the energy stored in this electric charge configuration?
- Positive charge Q is distributed uniformly along the x-axis from x=0 to x=a. A positive point charge q is located on the positive x-axis at x=a+r, a distance r to the right of the end of Q. Calculate the x-component of the electric field produced by the charge distribution Q at points on the positive x-axis where x>a. Express your answer in terms of the variables Q, a, r, and and appropriate constants. Calculate the magnitude of the force that the charge distribution Q exerts on q. Express your answer in terms of the variables Q, q, a, r, and appropriate constants. Calculate the direction of the force that the charge distribution Q exerts on q.Positive charge Q is distributed uniformly along the x-axis from x=0 to x=a. A positive point charge q is located on the positive x-axis at x=a+r, a distance r to the right of the end of Q. Calculate the x-component of the electric field produced by the charge distribution Q at points on the positive x-axis where x>a. Express your answer in terms of the variables Q, a, r, and and appropriate constants. Calculate the y-component of the electric field produced by the charge distribution Q at points on the positive x-axis where x>a. Express your answer in terms of the variables Q, a, x, and appropriate constants. Calculate the magnitude of the force that the charge distribution Q exerts on q. Express your answer in terms of the variables Q, q, a, r, and appropriate constants. Calculate the direction of the force that the charge distribution Q exerts on q.Two homogeneous rods with a length of 5 cm each are positioned as in Fig. a. Determine the magnitude and direction of the electric field vector at point P on the coordinates (5.0) cm, if the unit charge density is λ = 2.10-9 C / m! b. If an electron is placed at point P, what is the electric force that is experienced by the electron?
- Point P sets above an infinite line of charge 2 m in the positive z direction. The line of charge itself has a charge density ? of -5.0 x 10⁶ C/m. What is the magnitude of the electric field at point P?A continuous line of charge lies along the x axis, extending from x = + x0 to positive infinity. The line carries charge with a uniform linear charge density λ0. What are the magnitude and direction of the electric field at the origin?Positive electric charge is uniformly distributed along the y-axis with a linear charge density l. Consider the case where charge is distributed only between points y = +a and y = -a. For points between the +x-axis, graph the x-component of the electric field as a function of x, Ex (x), for values x = a/2 and x = 4a. Consider instead the case where charge is distributed along the entire y-axis with the same charge density l. Using the same graph as in part (a), plot the x-component of the electric field, Ex (x), as function of x for values of x between x = a/2 and x = 4a.
- The electric field everywhere on the surface of a thin, spherical shell of radius 0.775 m is of magnitude 897 N/C and points radially toward the center of the sphere. (a) What is the net charge within the sphere's surface? X If the net charge inside the sphere is moved to the center of the sphere would this change the value of the electric field on the surface? nC (b) What is the distribution of the charge inside the spherical shell? O The negative charge has an asymmetric charge distribution. O The positive charge has a spherically symmetric charge distribution. The negative charge has a spherically symmetric charge distribution. O The positive charge has an asymmetric charge distribution. 4Charge is distributed throughout a spherical volume of radius R with a density ρ = αr2, where α is a constant. Determine the electric field due to the charge at points both inside and outside the sphere.You are working as an intern for a meteorological laboratory. You are out in the field taking measurements with a device that measures electric fields. You measure the electric field in the air immediately above the Earth's surface to be 139 N/C directed downward. (Assume the radius of the Earth is 6.37 x 106 m.) (a) Determine the surface charge density (in C/m²) on the ground. C/m? (b) Imagine the surface charge density is uniform over the planet. Determine the charge (in C) of the whole surface of the Earth. (e) Determine the Earth's electric potential (in V) due to the charge found in (b). V (d) Determine the difference in potential (in V) between the head and the feet of a person 1.50 m tall. (Ignore any charges in the atmosphere.) V