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- A square surface of side length L and parallel to the y-z plane is situated in an electric field given by E(x, y, z) = E[i+ a(yj + zk)/V(y + z) ]. The square's sides are parallel to the y- and z-axes and it is centered on the x-axis at position Py. Its normal vector points in the positive x-direction. a is a unitless constant. Refer to the figure. The x-axis points out of the screen. Pr Part (a) Integrate to find an expression for the total electric flux through the square surface in terms of defined quantities and enter the expression. Part (b) For L = 8.2 m, E, = 309.9 V/m, and a = 9.9, find the value of the flux, in units of volt•meter.arrow_forwardConsider a right triangle ABC with the right triangle at vertex B. The charges at A, at B, and at C, are known to be 5 mC, 4 mC, and 7 mC, respectively. Given that the side AB is numerically equal to 91, in meters, and AC is thrice AB, find the magnitudes of the force and of the electric field at C.arrow_forwardConsider a right triangle ABC with the right triangle at vertex B. The charges at A, at B, and at C, are known to be 5 mC, 4 mC, and 7 mC, respectively. Given that the side AB is numerically equal to the last two digits of your student number, in meters, and AC is thrice AB, find the magnitudes of the force and of the electric field at C. (student number is 89)arrow_forward
- QUESTION 3 Problem Using the method of integration, what is the electric field of a uniformly charged thin circular plate (with radius R and total charge Q) at xo distance from its center? (Consider that the surface of the plate lies in the yz plane) Solution A perfect approach to this is to first obtain the E-field produced by an infinitesimal charge component of the charge Q. There will be several approaches to do this, but the most familiar to us is to obtain a very small shape that could easily represent our circular plane. That shape would be a ring. So for a ring whose charge is q, we recall that the electric field it produces at distance x0 is given by E = (1/ )(x0q)/ 24,2) Since, the actual ring (whose charge is dg) we will be dealing with is an infinitesimal part of the circular plane, then, its infinitesimal electric field contribution is expressed as = (1/ )(x0 We wish to obtain the complete electric field contribution from the above equation, so we integrate it from 0 to R…arrow_forwardConsider a right triangle ABC with the right triangle at vertex B. The charges at A, at B, and at C, are known to be 5 mC, 4 mC, and 7 mC, respectively. Given that the side AB is numerically equal to 86m, and AC is thrice AB, find the magnitudes of the force and of the electric field at A.arrow_forwardFor an electric dipole shown in the diagram the magnitude of charge q =78 μC. Find the value of the electric field at point P ( z>>d). Given that r(-) = 81 cm and r(+) = 66 cm. Note: Round off the answer to 2 decimal places.arrow_forward
- Consider a right triangle ABC with the right triangle at vertex B. The charges at A, at B, and at C, are known to be 5 mC, 4 mC, and 7 mC, respectively. Given that the side AB is numerically equal to the last two digits of your student number, in meters, and AC is thrice AB, find the magnitudes of the force and of the electric field at A.arrow_forwardFind the flux in N.m2.C-1 of a constant electric field E = (5.85x10^3) i + (2.712x10^3) j + (-7.4910x10^3) k N/C, passing through an area defined by the area vector A = (3.633x10^0) i + (1.5050x10^0) j + (-1.9920x10^0) k m2.arrow_forward= Problem 3. In a certain region of space, the electric field is constant in direction (say horizontal, in the x direction), but its magnitude decreases from 560 N/C at x 0 to 410 N/C at x= 25 m. Consider the gaussian surface in the form a cubical box of side 25 m where the box is oriented so that four of its sides are parallel to the field lines. (see figure below). ( = 8.85x10-¹2 C²/N·m², k = 9 x10° N·m²/C²). (a) Find the flux through the vertical surface on the left at x= 0. (b) Calculate the flux through the vertical surface on the right at x= 25 m. (c) Determine the average charge density within the cubical box. x=0 x = 25 m +25 m- Ëarrow_forward
- Given a scalar field with a function of f = Φ + Φz Calculate the slope in the direction of vector A if is A = x̂ + ŷ + ẑ Hint: You can answer it in cartesian coordinate or cylindrical coordinate.arrow_forwardAn electric field has a uniform value (doesn't change with position) that can be described by the following equation: E = (Aĵ + B k) N/C where A and B are given by the values below. A = 1.35 B = 1.80 There is a flat circular surface that is in the x-y plane and centered at the origin point (0,0,0). This surface has a radius of 1.65 m. Calculate the magnitude of the electric flux through the surface due to the electric field described above. Your units should be Nm²/C.arrow_forwardGiven that D = 10 x 3 3 a x(μC/m2), determine the total charge (in microcoulombs) enclosed in a cube of 2 m on an edge, centered at the origin and with edges parallel to the axes.arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning