Review, Concepts 12-17. (And little other stuff..)

1. Coulomb’s law is F_charge = kQq/r^2, where k is the constant 9*10^9 N*m^2/C^2. Q is the source charge, q is the test charge, r is the distance between the two point charges. The electric field acts over a distance. It extends outward from every charge and permeates all of space. A field is not a kind of matter. It has force lines which are perpendicular to the equipotential lines of the field. The direction of the force lines are from positive to negative electrode. If the distance between a negatively charged plate and a positively charged plate is lessened and the potential difference is held constant then the field will be stronger, if the distance is increased then the field will be weaker.

The factors that affect capacitors are expressed in the equation V = emf(1-e^-t/RC). The initial voltage, the resistance, the capacitance, and the emf all matter. The factors that affect the ability of the capacitor to store charge are the area is proportional to capacitance, and the distance between the plates is inversely proportional to the capacitance. The dielectric used is also a factor, which is directly proportional.

Ohm’s law is V = IR. The sum of the potential difference around a closed circuit is 0. ( LOOP RULE, Kirchoff ) The sum of the current entering a junction and the current leaving a junction is equal to 0. ( JUNCTION RULE, Kirchoff ) When resistances are connected in series, the sum of the resistances in the circuit will equal the equivalent resistance(the resistance that would be there if there were only one resistor) R_eq = R_1 + R_2 +.. etc. The sum of the voltage V1+V2+V3.. equals the total voltage V. Since this is true, then V = IR_eq. When in parallel, the reciprrocal of the total resistance equals the sum of the reciprocols of the individual resistances.. 1/R_eq = 1/R_1 + 1/R_2, etc. I, the total current is the sum of the partial currents. I = I_1 + I_2 + I_3.. etc. I = V/R_eq. If you have two parallel resistors, R1, R2, then the equivalent resistance is R1*R2/(R1+R2). P_loss is calculated by I^2*R

Electric motors, meters, and speakers work all on the principle of electromagnetism. Electric motors convert electrical energy into mechanical energy by using an alternating current to reverse the polarities every half revolution of the armature. Electric meters work because when the current is applied through, the needle will deflect since it is sensitive to the magnetic field. Speakers work by responding to the alternating current that runs though, which converts electric energy into sound energy. Faraday’s law is emf = -N*dMagFlux/dt. Lenz's law states that an induced emf always gives rise to a current whose magnetic field opposes the original change in flux. This is important when considering the direction of the induced current. If you have a coil and begin to slide a magnet in, the current induced will cause a magnetic field which opposes the motion of the bar magnet(which may also be said relative to the coil.) This is because if you insert the N pole of a bar magnet into the coil, an N pole is formed by the induced current on the side of the coil that the bar magnet is entering (use right hand rule). Upon having the magnet inserted in the coil, removing the magnet from the coil will cause a field that opposes the motion of the magnet leaving the coil. In order to solve problems for charged particles under the influence of magnetic fields, convert to the appropriate units first, and use the equation F = qvB sin theta. In order to determine the direction, you must determine if the particle has a positive or negative charge. Use your right hand rule if it’s positive, and use left hand if it’s negative. In order to use your right hand to determine the direction of the magnetic field about a straight wire, point your thumb along the wire in the direction of the conventional current, curl your fingers around the wire, this will be the direction of the magnetic field. In other words, it can only be CCW or CW about a straight wire, thus it will have no poles. For a solenoid, you must wrap your finger in the orientation of the wire wrapping. Your thumb will then point in the direction of the North pole.

Alternating current is current that follows a sinusoidal function. V = V0 sin 2pift, I_rms = sqrt(ave i0^2) = I_0/root(2) = .707I_0, V rms = sqrt(ave v0^2) = V_0/root(2) = .707V_0. A direct current is easier to deal with in the sense that you don’t need to find the root mean square value of the current or voltage. It is a constant flow of electrons instead of a fluctuating one.

The characteristics of a magnetic field of a permanent magnet are that the field goes from South to North internally. When considering the external magnetic field, it is North to South. At the ends of the magnet, it appears that a magnetic force line extends to infinity from the North pole and out and a line from infinity enters from infinity into the South pole. The factors that affect the strength of an electromagnet are the battery’s provided output, the field magnet’s strength, the proximity of the field magnets with the electromagnet, the coil looping space.

V_s/V_p = N_s/N_p = I_p/I_s, this is the transformer equation. A transformer is made up of a primary and secondary coil. An AC current must be supplied by the source emf to the primary coil. The primary coil is defined as the coil connected to the source of emf, and the secondary coil is defined as the coil connected to the load. Depending on which coil, primary or secondary, is the inner or outer coil, the transformer will ouput the source emf differently. If the primary coil is the outer coil and the secondary coil is the inner coil, it will act as a step-down transformer, one in which the output emf will be less than the source emf. If the primary coil is the inner coil and the secondary coil is the outer coil, it will act as a step-up transformer, one in which the output emf will be greater than the source emf. The number of turns in the coil is proportional to the induced emf’s magnitude.

Electromagnetic waves propagate by Huygen’s principle, the use of wavelets. They travel through space, they are transverse waves.

theta_incident=theta_reflected- law of reflection, For a plane mirror, light is reflected at the same angle that of which it strikes the mirror. The ray of light that strikes the mirror is referred to as the incident ray. The ray of mirror that reflects off the mirror is called the reflected ray. The angle of incidence and the angle of reflection, named respectively, are equivalent when taken from the normal. The normal is the line that bisects the full angle such that the angle of incidence and angle of reflection are equivalent. This normal is perpendicular to the plane mirror as well. The virtual image in a plane mirror is skewed proportionally to the actual image. The size of the virtual image depends on the distance between the actual image and the plane mirror. The further away the actual image is from the plane mirror, the smaller the virtual image appears. The closer the actual image is from the plane mirror, the more similar in size the virtual image is to that of the actual image. To apply the law of reflection to surfaces that are not flat, treat the point that the incident ray strikes as a plane mirror. From here, draw the tangent to that point and the plane mirror. The reflected ray can be obtained because of the law of reflection that states the angle of incidence is equivalent to the angle of reflection. For a concave mirror, when the object is located beyond the center of curvature, there will be a real image which is smaller, inverted and it will appear in front of the mirror. When the object is located at the center of curvature, there will be a real image, inverted, same size as object, located at the center of curvature which is in front of the mirror. When the object is located between the center of curvature and the focal point, there will be a real image, which is inverted and larger, in front of the mirror. When the object is located at the focal point, there will be no image because the reflected rays are parallel. When the object is located between the focal point and the mirror, there will be a virtual image which is erect, beyond the mirror, and larger. For a convex mirror, the images formed will always be virtual, erect, smaller, and beyond the mirror.

Refraction is the bending of light. When a ray of light is incident on an interface between two different mediums, a generalization can be made. If the index of refraction of the medium the incident ray travels through is greater than the index of refraction of the medium the emergent ray travels through, then the angle made by the incident ray to the normal will be less than the angle made by the emergent ray to the normal. If the index of the medium through which the incident ray travels through is less than that of the medium of which the emergent ray travels through, then it is just the opposite. Light tends to bend towards the normal when it passes from a material of lower index of refraction to that of a higher index. It tends to bend away from the normal as it passes from material of higher index to lower index. The index of refraction is a constant for a given material, which is the ratio c/v, where c is the speed of light in a vacuum and v is the velocity of light in that respective material.

Total internal reflection occurs when the angle of refraction is 90. This can only occur if the second medium of the interface has a lesser index of refraction. sin(theta_critical) = n_2/n_1, use this to calculate the critical angle between two substances.

Real images are formed by converged light rays. Virtual images are formed where light doesn’t actually reach. The rays reflect back into the eye.

The eye focuses on objects at different distances by the process of accommodation. To focus on a nearby object, the muscles contract, causing the center of the lens to be thicker, which then shortens the focal length. For a far away object, the muscle relaxes so that the lens is thinner. This increases the focal length. A nearsighted eye has the problem that the eyeball is too long, or sometimes the curvature of the cornea is too great. The objects are focused in front of the retina then. This can be corrected with a diverging lens, since it causes the light to diverge then be refocused at the retina. A far sighted eye is just the opposite. The eyeball is too short, or the curvature of the cornea isn’t curved enough. This can be corrected with a converging lens.

The major classifications of energy in the electromagnetic spectrum are radio, microwave, infrared, visible, ultraviolet, x-rays, gamma rays.

When white light is passed through a prism, the index of refraction depends on wavelength, so the different wavelengths(colors) are bent to varying degrees. Violet light is bent the most since index of refraction is greater for shorter wavelengths. Red is bent the least. When light passes through a diffraction grating, the light diffracts at every opening between the parallel lines of the grating. Since it diffracts the light so much into its component wavelengths, the pattern ends up being a spectrum

Line spectrum are characteristic of gaseous compounds at normal temperature. This occurs when the gas is heated or a large electric current is applied to the compound. Light from heated solids such as a lightbulb’s filament and even gases under high pressure produce a continuous spectrum. Absorption lines also occur since atoms and molecules can absorb light at the same lambdas that they emit light at.

Light behaves like a wave in the sense that it exhibits interference and diffraction patterns. It behaves like a particle in the sense that it is affected by gravity and it quantized, apparently having no rest mass.

The Bohr model of the atom makes two important assumptions. An electron may exist only in certain particular orbits; when it is in one of the permitted orbits it does not radiate even though it is accelerating. An electron may suddenly jump from an outer to an inner orbit; when it does so, it loses energy, which is radiated as a single photon. He applied Planck’s quantum ideas to the hydrogen atom. His success in predicting the exact frequencies of the hydrogen spectrum was the convincing evidence that made quantum theory accepted.

Quantum theory explains spectra and the photoelectric effect by stating that different materials have different work functions; that is that there is a defined quantity of energy necessary for electron/photon emission. By the equation E = hc(1/lambda_0 – 1/lambda), where lambda_0 is the threshold wavelength, you can see that if 1/lambda exceeds 1/lambda_0, then there will be a negative value for E which is nonsensical. Materials have this characteristic An idealized blackbody absorbs all the radiation falling on it. With regards to the photoelectric effect, if the light intensity is increased, the number of electrons as well as their maximum kinetic energy increases. The frequency does not affect the KE_max. hf = KE + W. There is a specific frequency for each material where no electrons will be ejected until it is reached.