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# Electric & Magnetic Fields

### Electric field lines & equipotential lines

Draw a picture of the electric field lines generated by a collection of two positive charges, both of charge q = 1. Center one at (1,0) and the other rat (-1,0). What happens to the electric field at the origin? (the point 0,0) Draw a few equipotential lines. Remember, these are the curves that circle the charge distribut

### Surface force on electrically charged balloon

A balloon made of light conducting material could be kept approximately spherical by connecting it to a high voltage supply. The balloon has radius 0.05 m, and the dielectric breakdown field to produce spark in air is E_b = 3?10^6 V/m a) What is the maximum permissible voltage? b) What gas pressure, in atmospheres, insi

### Solve: Electric Potential Difference

Question: Two protons are moving directly towards one another. When they are very far apart, their initial speeds are 3.00 x 10^6 m/s. What is the distance of closest approach?

### Energy in the Field of an Electric Dipole

Show that the energy in the field of an electric dipole of moment p outside a sphere of radius R is p^2/(12*pi*epsilon nod*R^3).

### Four charges placed at the corners of a square

Find the magnitude of the electric field at point d. (Data: q= 0.750 mC, L= 0.40 m)

### Electric Field & Magnitudes

The lines show the equipotential contours in the plane of three point charges, Q1, Q2, and Q3. The values of the potentials are in kV as indicated for the +5, 0, and -5 kV contours. The positions of the charges are indicated by the dots. the work required to move a charge of -0.51×10-12C from i to b is 3.06×10-9 J a: Ca

### Expression Point Charges

y l l a (+q) l l -------l--------x l -a (+2q) l l Two point charges are fixed on the y-axis at the locations shown in the figure above. A charge of +q is located at y = a and a charge of +2q is located at y = -a. Express your answers to a an

### Impossible electrostatic field, charges and work

See attached file for full problem description. 8. (a) Three charges are situated at the corners of a square (side a) as shown in Figure 2.41: (a) how much work does it take to bring in another charge, +q, from far away and place it in the fourth corner? (b) How much work does it take to assemble the whole configuration of

### Electric field above surfaces

Electric field above surfaces. See attached file for full problem description. 1. find the electric field a distance z above one end of a straight line segment of length L, which carries a uniform line charge lamda. check that you formula is constistent with what you would expect for the case z >>L. 2. Find the electric fie

### Equipotential curves surfaces

Hello, The problem states: V(x,y,z) = A(x^2 - 3y^2 + z^2) E(vector) = -2Ax, 6Ay, -2Az A = 640 the E field at a point (0,0, 0.250) = (0,0,-320) It says: In every plane parallel to the x-z plane, the equpotential contours are circles. What is the radius of the equipotential contour corresponding to V = 1280 V

### What force is needed on a charged sphere hanging in between two parallel vertical plates?

A small sphere with mass 1.10 g hangs by a thread between two large parallel vertical plates 5.00 cm apart (see the diagram in the attached file). The plates are insulating and have uniform surface charge densities +&#963; and -&#963;. The charge on the sphere is q = 8.60 * 10-6 C. What potential difference between the plates

### Electric Field, Radioactivity & X-Ray Wavelength

1. The drawing shows the potential at five points on a set of axes. Each of the four points is 7.0 x 10^-3 mt from the point of origin. From the data shown find the magnitude and the direction of electric field in the vicinity of origin. (See attached for diagram) 2. A 0.5 kg tumor is being irradiated by a radioactive sou

### Electron moving in the field of parallel plate capacitor

An electron is released from rest at the negative plate of a parallel plate capacitor. The charge per unit area on each plate is phi= 1.8 x 10 ^-7 C/m^2, and the plates are separated by a distance of 1.5 x 10^-2 m. How fast is the electron moving just before it reaches the positive plate?

### Parallel plates capacitor

Two parallel plates are .005m apart and are each 2m2 in area. The plates are in vacuum and an electric potential difference of 10,000V is applied across them. 1) Find the: a)capacitance, b)the charge on each plate c)the electric field intensity in the space between, and d) the stored energy. 2) If a dielectric mater

### Magnetic field at the centre of a rotating uniformly charged hemispherical shell.

3. A uniformly charged hemispherical shell is rotating with angular speed w (omega) about its symmetry axis as shown. Use the Biot-Savart Law to find the magnetic field at the center of the sphere (point P). Begin by discussing the direction of B. See attached file for full problem description.

### Circuits

See attached file for full problem description. Three point charges are located along the circle of radius. Derive the expression for the electric field in the center.

### Electromagnetic Waves and Electric Fields

Suppose a plane electromagnetic wave has a wavelength of 50 m and the electric field vibrates with an amplitude of 22 V/m. Calculate the frequency of the wave, the amplitude of B. Write an expression for B in a the form B=Bo cos(kx-w(omega)t) with numerical values for B0, k, and w. See attachment for better formula representatio

### Force on a current carrying conductor due to magnetic field.

In this problem i am not sure if you can just use the right hand screw rule The cube is 40 cm on each edge. Four straight segments of wire - ab, bc, cd, and da - form a closed loop that carries a current I = 5 A, in the direction shown. The loop is placed in a uniform magnetic field of magnitude B = 0.020 T in the positive y

### Mutual inductance and inductance of a transformer primary

1) How would you arrange two flat circular coils so that their mutual inductance was a) greatest b) least (without separating them by a great distance)? 2) If you are given a wire of such length that you can make only two loops out of it, how would you shape this wire to obtain a) the greatest; b) the least self-inductance?

### Conductor with varying cross section areas

Suppose that a current-carrying ohmic metal wire has a cross-sectional area that gradually becomes smaller from one end of the wire to the other. How do drift velocity, current density, and electric field vary along the wire? Please explain with the help of equations to support explanation.

### Point Charge and Coordinate System

A point charge Q is located at the origin. Express the potential in both rectangular and cylindrical coordinates, and use the gradient operation in that coordinate system to find the electric field intensity. The result may be checked by conversion to spherical coordinates.

### Magnetic field at the core of a solenoid

A solenoid that is 75 cm long produces a magnetic field of 2.1 T within its core when it carries a current of 6.8 A. How many turns of wire are contained in this solenoid?

### Electric field near grounded conducting cylinder

Consider a grounded conducting cylinder of radius, a, in a uniform electric field, E0 in the x direction. Let the cylinder axis be the z-axis. Using the Laplace's equation solution in cylindrical coordinates, find the potential and the induced surface charge.

### Finding the energy density of an electric dipole

(See attached file for full problem description) --- Suppose we have a sphere of radius, a, centered on a dipole, p, at the origin. Integrate the energy density of the field outside the sphere, and show that U=p^2/(12 pi Eo a^3). ---

### How far must two point charges - one positive and one negative be separated for the specified value of electric potential energy of the system.

How far must the point charges q1 = +7.22 µC and q2 = -22.9 µC be separated in cm for the electric potential energy of the system to be -159 J?

### A large conducting spherical shell has fixed surface charge density, has a small circular hole in the surface. Using integration over the surface of the sphere find the electric field in the hole at its center.

A large conducting spherical shell of radius a, and fixed surface charge density (sigma), has a small circular hole in the surface of radius b<<a. [Note the cap of radius b is measured on the curved surface, not the chord, so that the angle subtended, alpha, at the center of the sphere from the center of the hole to the edge of

### Electromagnetic Theory: Magnitude and Direction of Force

(Refer to attached picture file) A uniform B field of magnitude 0.0769 T is directed as shown in the diagram. A straight wire segment 15.0 cm long lies in the plane of the paper and carries a current of 28.7 A from the upper right to the lower left. a) On the diagram sketch the direction of the force on the wire. b) Find

### Electromagnetism: Force on moving charge in a magnetic field

1. In an experiment with cosmic rays, a vertical beam of particle that have charge of magnitude 3e and mass 12 times the proton mass enters a uniform horizontal magnetic field at 0.250 T and is bent in a semicircle of diameter 95.0 cm a) Find the speed of the particles and the sign of their charge. b) Is it reasonable to ignor

### Magnetic field of a solenoid and a long straight wire

3. The current in a solenoid with 22 turns per centimeter is 0.50 A. The solenoid has a radius of 1.5 cm. A long, straight wire runs along the axis of the solenoid, carrying a current of 23 A. Find the magnitude of the net magnetic field a radial distance of 0.69 cm from the straight wire. mT I don't understand how the so

### Charged pendulum in electric field

A 1.00 g cork ball with charge 2.00 uC is suspended vertically on a 5.00 m long, light string in the presence of a uniform, downward-directed electric field of magnitude E = 1.00 x 10^5 N/C. If the ball is displaced slightly from the vertical, it oscillates like a simple pendulum. a) Determine the period of this oscillation.