# 4. We know from electrostatics that if we have a scalar electrostatic potential V, then there exists an electric field... 4. We know from electrostatics that if we have a scalar electrostatic potential V, then there exists an electric field that satisfies: Of course, not all vector fields can be written as the gradient of a scalar function. (a) Show that the electric field given below is not the result of an electrostatic potential (b) Just because this electric field can't come from an electrostatic potential, it doesn't mean it can't exist - it just can't be created by static (i.e. unmoving) charges. The local form of Faraday's law (quoted below) describes how such an electric field can come from a time-varying magnetic field. Use this to show that this particular electric field can come from a uniform magnetic field that is changing linearly with time (such as within a solenoid with a current changing linearly in time. dt ##### Add Answer of: 4. We know from electrostatics that if we have a scalar electrostatic potential V, then there exists an electric field...
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• ### We know from electrostatics that if we have a scalar electrostatic potential V, then there exists an electric field tha... We know from electrostatics that if we have a scalar electrostatic potential V, then there exists an electric field that satisfies: Of course, not all vector fields can be written as the gradient of a scalar function. (a) Show that the electric field given below is not the result of an electrostatic potential. E(x, y, z) = ( 3.0m,2 ) ( yi-TJ (b) Just because this electric field can't come from an electrostatic potential, it doesn't mean it can't exist...

• ### State the condition uder which the electric field, E can be presented by the gradient of a scalar... Q1. Electromagnetism State the condition uder which the electric field, E can be presented by the gradient of a scalar potential, V. Show that in electrostatic situations the remaining Maxwell equation can be written as 0 where p is the charge density. Prove that has a unique solution inside a closed surface, S, if V is specified on S Explain how the uniqueness of the soltion of ( is exploited in the method of images State the condition uder which...

• ### We can combine the scalar potential V and the vector potential A to a combined 4-vector potential: Calculate the components of a 4x4 electromagnetic field tensor: with the contravariant vector: fro... We can combine the scalar potential V and the vector potential A to a combined 4-vector potential: Calculate the components of a 4x4 electromagnetic field tensor: with the contravariant vector: from the electric field and the magnetic field We were unable to transcribe this imageWe were unable to transcribe this imageい() ct OA Ot We were unable to transcribe this image い() ct OA Ot

• ### State the condition uder which the electric field, E can be presented by the gradient of a scalar... State the condition uder which the electric field, E can be presented by the gradient of a scalar potential, V. Show that in electrostatic situations the remaining Maxwell equation can be written as 0 where p is the charge density. Prove that (") has a unique solution inside a closed surface, S, if V is specified on S Explain how the uniqueness of the soltion of ( is exploited in the method of images charge q is placed at (a,...

• ### I wanna know how to solve theses.. professor.. 8. Inside a perfect conductor, there is no... I wanna know how to solve theses.. professor.. 8. Inside a perfect conductor, there is no electric field, i.e., E =0.(20) a. Show that the electrostatic potential is constant in the surface of the conductor. (5) b. Show that the electric field just outside the conductor is perpendicular to its surface. (5) c. There is a hollow (vacuum) cavity lying inside a conductor. What is the electric field in the hollow volume? (10) 9. There is an infinitely long solenoid...

• ### how did we get the following equation (1.9) from maxwells equations at e at where p is the density of free charges and j is the density of currents at a point where the electric and magnetic fie... how did we get the following equation (1.9) from maxwells equations at e at where p is the density of free charges and j is the density of currents at a point where the electric and magnetic fields are evaluated. The parameters and are constants that determine the property of the vacuum and are called the electric permittivity and magnetic permeability respectively The parameter c-1/olo and its numerical value is equal to the speed of light in vacuum,c 3 x...

• ###  2. In the previous problem, how long after switch is closed until the magnetic field... 2. In the previous problem, how long after switch is closed until the magnetic field is stable? Answer: (a) 1.38 ms. (6) 1.85 ms (c) 2.33 ms. (d) 2.79 ms. (e) 341 ms. (1) -  3. An AC generator is connected to a circuit. The generator's emfis E(0) - 152 V sin(at). If the maximum current that results is 150 mA circuit, -5.01 x 10rad/s and the phase angle is -85.6 degrees, complete the following (0) = sin...

• ### Number of rectangular elements 3.000 show rectangular elements Click and drag figure to rotate ▼ Question 8 Give a symbolic expression for the magnetic field B at the center of an infinites... Number of rectangular elements 3.000 show rectangular elements Click and drag figure to rotate ▼ Question 8 Give a symbolic expression for the magnetic field B at the center of an infinitesimal area element, such as the one depicted in Fig. 30.1.2 (repeated below). Enter the symbolic expression in the blue box below (using al or some of the following symbols: μο-1 (current in wire), π. y (distance of area element from wire), L b, a), and enter a unit...

• ### A long straight wire has a hollow spherical conductor of radius R hanging from its end. The wire carries a downward current I. You are curious about the magnetic field, if any, that might exist ju... A long straight wire has a hollow spherical conductor of radius R hanging from its end. The wire carries a downward current I. You are curious about the magnetic field, if any, that might exist just outside the "equator" of the sphere, i.e. the circle created by the intersection of the surface of the ball with a horizontal plane through its center, shown by the solid line a) What is the amount of charge on the sphere as a function...