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# Electric & Magnetic Fields

### Physics: Cyclotron Frequency

An electron with velocity 4.00×10^6 m/s enters in a magnetic field which is perpendicular to the velocity. A magnetic force 5.50×10-4 N acts on the electron and force it to move on a circular trajectory. The frequency of the electron's circular motion is called cyclotron frequency. Find the value of the cyclotron frequency. (H

### Electric Field in Matter

See the attached file. An electromagnetic wave with frequency f = 10^6 Hz ravels along the z-axis in aluminum. In this medium sigma=38*10^6 (Ohm*m)^(-1) , e = e0 and mu=mu0 At the surface of the aluminum the electric field amplitude/polarization is E in the x direction. Write an expression for the electric field inside

### Potential between concentric conducting spheres

A conducting sphere of radius r1 is suspended by a perfectly insulating thread inside and concentric with a larger conducting sphere of radius r2 and the space between the spheres is a vacuum. A charge q is deposited on the outer sphere. What is the potential difference (as would be measured by a voltmeter) between the two spher

### Electricity, Magnetism and Waves.

A spherically symmetric volume charge distribution is given by Rho® = k*r for r (less than or equal to) a 0 for r > a Find: a) what is the electric field both inside and outside the sphere b) what is the potential at any point inside the sphere c) How much energy was required to

### Magnetism and Dipoles in a Magnetic Field

- A magnetic dipole m = −m0 ˆ z is situated at the origin, in an otherwise uniform magnetic ﬁeld B = B0 ˆ z. - Show that there exists a spherical surface, centered at the origin, through which no magnetic ﬁeld lines pass. - Find the radius of this sphere, and sketch the ﬁeld lines, inside and out. See the attache

### Current to Suspend a Wire

How much current would you need to suspend a wire in the magnetic field from a magnet? The magnet has a B-field of about 1000 Gauss in the gap; the wire's length is about 6 cm and has a mass of 50 grams. See the attached diagram.

### Uniform Magnetic Field

You want to create a uniform (constant and parallel) magnetic field in a small volume of space. The field should be 500 Gauss. You can get a current of 0.8 Amperes from a power source, and you must choose one of the following methods (only one method is correct): a. A single long straight wire, at distance r from t

### Proton's Kinetic Energy is figured

A proton has a kinetic energy of 150 MeV. (a) How fast is it going? (b) What magnetic field (magnitude and direction) would be required to make it go around a bend to the right with a 0.6-meter radius?

### Magnetic Components in a Field

The x, y, and z components of a magnetic field are Bx = 0.10 T , By = 0.15 T , and Bz = 0.17 T. A 25-cm wire is oriented along the z axis and carries a current of 4.3 A. What is the magnitude of the magnetic force that act on this Wire.

### The Seperation of Variables

Solve Laplace's equation by separation of variables in cylindrical coordinates. Assume symmetry about the z axis and no z dependence. Check the result by comparing to an infinite line charge.

### The Magnitude and the Direction of an Electric Field

What are the magnitude and direction of the electric field at a point midway between a -8.0 µC and a +6.0 µC charge 4.0 cm apart? Assume no other charges are nearby.

### The Magnitude and Sign of a Point Charge

A point charge (m = 1.0 g) at the end of an insulating string of length 46 cm is observed to be in equilibrium in a uniform horizontal electric field of 9200 N/C, when the pendulum's position is as shown in attached diagram, with the charge 2.0 cm above the lowest (vertical) position. If the field points to the right as shown in

### Resultant of Magnetic Fields

Two infinitely long straight currents are parallel to the z axis. One of them, carrying a current I_1, intersects with the xy plane at the point (x_1, y_1); the other with current I_2 intersects the xy plane at (x_2, y_2). Find the resultant B produced by them at any field point.

### Physics - Electrostatics Problems

Two point charges lie along the y axis. A charge of q1 = -11 micro Coulombs is at y=8.0m and a charge of q2 =-4.0 micro Coulombs is at the y=-1.0m. Locate the point (other than infinity) at which the total electric field is zero.

### Electrostatics

Two point charges lie along the y axis. A charge of q1 = -11 micro Coulombs is at y=8.0m and a charge of q2 =-4.0 micro Coulombs is at the y=-1.0m. Locate the point (other than infinity) at which the total electric field is zero.

### E Field Electronic Field Drawing

Simple drawing of the fields of two particles in relation to each other as indicated in the attachment. Guidelines are: - The closer the lines are together, the stronger the E in that region - The field lines indicate the direction of E; the field points in the direction tangent to the field line at any point - The lines a

### Finding the Electric Field of a Uniformly Charged Ring

A uniformly charged ring of radius R has a total charge Q. 1) What is the magnitude and direction of the electric field along the axis of the ring? 2) What is electric field potential along the axis of the ring? 3) What is the electric field at the center of the ring? 4) What is the electric potential at the center o

### Electrostatic: Spherical charge distribution

Please see the attachment for description. 1.) What is the total charge inside a shpere of radius 1 and center in the origin. 2.) What is the electric field magnitude for points r>R 3.) What is the electric field magnitude for points r<R 4.) At what distance r0 the magnitude of the electric field is the largest. 5

### Capacitor with a dielectric slab between the plates

A slab of dielectric of thickness t is inserted into a parallel plate capacitor of plate separation d and plate area A as shown in the fig (see attachment f.10-19). The surfaces of the slab are parallel to the plate surfaces. Find D, P and E as functions of x and plot your results. (Express them in terms of Q). Find capacitance

### Lorentz Force on an Electron

There is a positron and an electron and a uniform magnetic field is applied to them. One curls to the right and one curls to the left. Deduce which one of them curls to the right, and which one curls to the left, and the direction of the magnetic field?

### Solenoid is designed to produce a magnetic field

2) A solenoid is designed to produce a magnetic field of 0.027T at its centre. It has a radius of 1.4cm and a length of 40cm, and the wire can carry a maximum current of 12A. i) How many turns per length must the solenoid have? ii) What total length of wire is required?

### Magnetic Field at the Center of Rotating Charged Disk

A thin disk of dielectric material with radius a has a total charge +Q distributed uniformly over its surface. It rotates n times per second about an axis perpendicular to the surface of the disk and passing through its centre. Find the magnetic field at the centre of the disk.

### Dielectric Inserted between Plates of Capacitor

A constant potential difference of 12 V is maintained between the terminals of a 0.25-uF parallel-plate air capacitor. 1.) A sheet of Mylar is inserted between the plates of the capacitor, completely filling the space between the plates. When this is done, how much additional charge flows onto the positive plate of the capaci

### Negative Charge on Circular Disk

A thin circular disk with a circular hole at its center (called an annulus) has inner radius R1 and outer radius R2. The disk has a uniform positive surface charge density σ on its surface. i) Determine the total electric charge on the annulus. ii) If the annulus lies in the y-z plane with its center at the origin find the magn

### Electric Potential of Disk with Uniform Surface Charge

Please see the attachment for full problem statement. A disk with radius R has uniform surface charge density. By regarding the disk as a series of thin concentric rings, calculate the electric potential V at a point on the disk's axis a distance x from the center of the disk. Assume that the potential is zero at infinity.

### Determining Electric Potential Created from Two Point Charges

Two point charges, q1= 2.00 nC and q2= -6.80 nC, are 0.100 m apart. Point A is midway between them; point B is 0.080 m from q1 and 0.060 m from q2 (see the attachment). Take the electric potential to be zero at infinity. Find the potential at point A. Find the potential at point B. Find the work done by the electric

### Electric field due to two long uniform lines of charge

A very long uniform line of charge has charge per unit length 4.82 micro-Coulombs/m and lies along the x-axis. A second long uniform line of charge has charge per unit length -2.58 micro-Coulombs/m and is parallel to the x-axis at y1 = 0.398 m. What is the magnitude of the net electric field at point y2 = 0.216 m on the y-

### Small sphere hanging from thread near charged sheet

A small sphere with a mass of 2.00×10^-3 g and carrying a charge of 4.80×10^ -8 C hangs from a thread near a very large, charged conducting sheet, as shown in the figure (see the attachment). The charge density on the sheet is &#8722;2.40×10^(-9) C/(m^2) . Find the angle of the thread.

### Electric Field due to a Uniformly Charged Circular Arc

The circular arc of a radius a shown in figure 3-7 lies in the xy plane and has a constant linear charge lamda and center of curvature at the origin. Find E at an arbitrary point on the z axis. Show that when a curve is a complete circle your answer becomes. See attached.

### Electrostatics: Electric Field Due to Infinite Line Charge

A uniform infinite line charge is parallel to the z axis and intersects the xy plane at the point (a,b,0). Find the rectangular components of E produced at the point (0,c,0). See attachment for further details to the question.