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# Electric & Magnetic Fields

An electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the surrounding force of an electrically charged particle exerted on other electrically charged objects. The concept of an electric field was first introduced by Michael Faraday.

The electric field is a vector field with SI units of newton’s per coulombs. The strength of the field at a given point is defined as the force that would be exerted on a positive test charge of one coulomb placed at that point. The direction of the field is given by the direction of that force.

An electric field that changes with time influences the local magnetic field. The electric and magnetic fields are not completely separate phenomena’s. What one observer perceives as an electric field, another observer in a different frame of reference perceived as a mixture of electric and magnetic fields.

A magnetic field is a mathematical description of the magnetic influences of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude. The magnetic field is most commonly defined in terms of the Lorentz force it exerts on moving electric charges.

Magnetic fields are produced by moving electric charges and intrinsic magnetic moments of elementary particles with a fundamental quantum property, their spin. In special relativity, electric and magnetic fields are two interrelated aspects of a single object. This is called the electromagnetic tensor.

Magnetic fields are most often encountered as an invisible force created by permanent magnets. These magnets pull on iron objects that attract or repel other magnets. Magnetic fields are widely used throughout modern technology.

## BrainMass Categories within Electric & Magnetic Fields

### Ampere's Law Solutions: 43

Ampere's Law is the law that for any states closed loop circuit, the sum of the length elements times the magnetic field in the direction of the length element is equal to the permeability times the electric current enclosed in the loop.

### Electric and Magnetic force on an electron

An electron orbiting in an atom in a circular orbit of radius r0, moving with velocity v. The motion produces a magnetic field within the orbit of roughly the value at the center. Answer following questions using nonreletivistic approach. (a) Use the central value of B to find the magnitude of the force FB that acts on a sec

### Levitation in the electric field near the surface of the earth.

The electric field is defined as the electrostatic force divided by the charge experiencing this force. The Earth's electric field is directed radially inward and is about 150 N/C at the Earth's surface. This arises because in a region of the atmosphere known as the ionosphere, parts of the spectrum of the radiation from the sun

### Using Green's function to solve Poisson's equation

This solution addresses a problem on how to relate a Poisson's equation and the Green's function. The original problem can be found at http://farside.ph.utexas.edu/teaching/em/lectures/node31.html

### An Air-Filled Toroidal Solenoid

An air-filled toroidal solenoid has a mean radius of 14.9 cm and a cross-sectional area of 4.95cm2 (see the attached figure). The current flowing through it is 12.1A, and it is desired that the energy stored within the solenoid be least 0.394J. What is the least number of turns that the winding must have? (A whole number to t

### Electrostatic Potential

Another illustration of the use of Legendre polynomials is provided by the problem of a neutral conducting sphere (radius r_0) placed in a (previously) uniform electric field (see attachment). The problem is to find the new, perturbed, electrostatic potential. If we call the electrostatic potential v, it satisfies [see the att

### Finding the location where the total electric force on a given positive charge is zero in a region of two negative charges.

A charge of -3.50 nC and a charge of -6.30 nC are separated by a distance of 70.0 cm. Find the position at which a third charge of +7.40 nC can be placed so that the net electrostatic force on it is zero.

### Magnitude/Direction of Electric Field

Using the attached diagram, please help me with the following. (a) Find the magnitude/direction of the electric field at the center of the configuration of charges. (b) Using the result from (a), find the magnitude and direction of the force on an electron placed at the center of the configuration.

### Electrostatics: Capacitor

The plates of a parallel plate capacitor are 1 mm apart, each has an area of 1000 cm^2, and they are kept connected across a 600 V battery. Take the medium to be air (Ke = 1). (a) If the plates are moved apart until the separation is 2 mm, how much mechanical work is done and how much energy is returned to the battery?

### Magnatic Field at a Disk Center

A small/thin circular conducting disk that can carry total current, as represented by 'I'. The current path is circular at every distance from the center of the disk, and the each circle center is the disk center. Find the magnetic field at the disk center, assuming the current density is: 1. Constant 2. Inversely proporti

### What is the net electric potential at the origin?

What is the net electric potential at the origin due to the circular arc of charge Q1 = + 7.21 pC and the two particles of charges Q2 = 4.00 Q1 and Q3 = - 2.00 Q1? The arc's center of curvature is at the origin and its radius is R = 2.00 m; the angle indicated is theta = 20.0 degree. Please refer to the attachment for complet

### Interference of Electromagnetic Plane Waves

** Please see the attached file for the complete problem description ** Two plane waves that are spatially and temporally coherent propagate in the x-z plane and intersect at an angle such that each wave makes an angle (please see the attached file) with the z-axis. The figure below shows the k-vectors associated with the two

### Near field (electric or magnetic) or far field

Discuss the nature of the wave impedance at a distance of 1 metre from the following devices: (i) A microwave oven operating at a frequency of 2.45 GHz. (ii) A radio-frequency heat-sealer operating at 27 MHz. (iii) The field coil of a 'deactivation pad' operating at 60 kHz. The pad is used in retail stores to demagnetise

### Capacitors and Conservation of Energy

In a parallel plate capacitor, the electric field on the left side and, on the right side of the plates is: a) 4Ï?kQ/A b) -4Ï?kQ/A c) zero d) NA 2) Two balls of mass m = 1 kg each and carrying charges Q = 1C each are fixed at a distance r = 1m from each other as shown. Find the final velocity of the ball (1) after it is

### Physics: 5 Problems on electrostatics.

4a. Consider the parallel plate capacitor, where the surface charge density is 0.02 uC/m^2, and the distance between the plate is 0.01m. What is the potential difference between the two plates? 4b. What would be the change in potential energy of the electron as it moves from the negative plate to the positive plate? 4c.

### The Force experienced by an Electron in a Uniform Electric Field

What force is experienced by an electron (charge magnitude 1.6 x 10^-19 Coulomb) in the electric field created by a 8-volt battery (assume negligible internal resistance) in a uniform conducting wire 2.5 meters long?

### Physics: Magnetic field of two parallel conductors

Two long straight, parallel wires are 2.00 m apart, and each carries a current of 10 mA. Find the magnitude and direction of the magnetic field at a point midway between the wires if the currents are (You must show your reasoning/work) (a) in the same direction and (b) in opposite directions

### Electron's Motion in a Magnetic Field

(Please see attached figure) The uniform 32.0 mT magnetic field in the figure points in the positive z-direction. An electron enters the region of magnetic field with a speed of 5.50 * 10^6 m/s and at an angle of 30 degrees above the xy-plane. 1. Find the radius r of the electron's spiral trajectory. 2. Find the pitch

### Ranking the locations in order of strength of a magnetic field

An infinitesimal current element located at the origin (x = 0, y = 0, z = 0) carries current (I) in the negative z-direction. Rank the following locations in order of the strength of the magnetic field that the current element produces at that location, from largest to smallest value 1. x = 0 , y = 0, z = L 2. x = L, y =

### Determining Magnitude and Direction of a Vector

A proton moving in a uniform magnetic field with v1 = 1.19 * 10^6 i [hat] m/s experiences forces F1 = 1.49 * 10^-16 k [hat] N. A Second proton with v2 = 2.12 * 10^6 j [hat] m/s experiences F2 = -3.85 * 10^-16 k [hat] N in the same field What is the magnitude of B? B=__________mT What is the direction of B [vector]? G

### Physics: Position and magnitude of electric charge

A +3.0 charge is at and a -1.0 charge is at . At what point or points on the x-axis is the electric potential zero? X = ___________ cm A -2.0 charge and a +2.0 charge are located on the x-axis at and , respectively. At what position or positions on the x-axis is the electric field zero? At what position or pos

### Consider the situation that the charge is not distributed uniformly along the bar.

Please show all the steps and calculations. Consider the situation that the charge is not distributed uniformly along the bar. The bar is 4.531*10^-3 m long and is charged with 6.918*10^-9 C. We want to calculate the electric field strength at point P that is 1.115*10^-2 m away from the center of the bar. Assume that the char

### Angle of total electric field due to three charges

Show all workings. A charge of +10.7 micro-Coulombs is placed at the origin of a coordinate system. Another charge of -12.6 micro-Coulombs is placed at x = +0.19 m, y = +0.1 m. A third charge of +13.2 micro-Coulombs is placed at x = -0.19 m, y = 0 m. At what angle is the total electric filed is directed at the the point x = 0

### Physics: Magnitude and the direction of an electric field

** Please see the attached file for the complete problem description ** Please provide answers with complete explanations

### Electric field between two charged parallel plates

Please help with the following problem. A uniform electric field exists in the region between two oppositely charged parallel plates 1.53 cm apart. A proton is released from rest at the surface of the positively charged plate and strikes the surface of the opposite plate in a time interval 1.47 * 10^-6 s apart. Part A: Fi

### Force on a proton, x and y components, magnitude, acceleration

** Please see the attached file for clarity ** Please provide answer and complete explanation and steps. The electric field at a point in space is 900 900 . Part A What is the x-component of the electric force on a proton at this point? Express your answer numerically, in newtons, to three significant figures.

### Magnetic induction at the center

A square of edge 'a' lies in the xy plane with the origin at its center. Find the value of the magnetic induction at any point on the z axis when a current I' circulates around the square. Show that your result gives the value 2(sqrt 2) Uo*I' /pi*a or the induction at the center. See attachment for better formula representation.

### Electric Fields (Line, Loop and Disc)

Would you please help me to understand the following questions? (1) Consider a line of charge, density ?, length L, lying along the x-axis from 0 to L. Find the electric field E a distance z along the z-axis. What is the limiting value when z >> L ? (2) Find the electric field, E a distance z above a circular loop of charg

### A Hybrid || plate capacitor is examined & problems solved

A parallel plate capacitor consists of two plates of surface area (A) spearated by a distance (d.) This capacitor is in turn connected in series to a DC supply of voltage V volts. A slab of material with permitivity k and thickness d/2 is placed between the plates as shown (SEE PROBLEM ATTACHMENT). We can divide the dielctric be

### Electric force or field due to several charges

1- Calculate the force (direction and magnitude) on Q3 due to two other charges shown in the figure. 2- What is the magnitude of the electric field experienced by an electron in the hydrogen atom? In the ground state, their average separation is one Bohr radius (0.53x10^(-10) m).

### State Energy: Consider an electron with spin magnetic moment u_s

Consider an electron with spin magnetic moment u_s in a strong magnetic field B_z in the z direction. The potential for an electron with spin magnetic moment u_s in a magnetic field B is V=-u_s . B where u_s = -((g_s)(u_B))/(hbar) . S Thus the Hamiltonian is H_0 = ((g_S)(u_B))/(hbar) . B . S = ((g_s)/2)(u_B) . B . sigma