Electricity and magnetism berkeley physics course free download

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November 13, December 13, Previous post Dynamics 12th edition solution manual. Next post Electrochemical methods solutions manual pdf. January 9, January 6, January 1, December 29, December 21, Figure Magnetic force on a moving charge in a current-carrying conductor. We can determine the force exerted on one wire due to the magnetic field set up by the other wire. Wire 1, which carries a current I1, G G creates a magnetic field B1 at the location of wire 2.

The direction of B1 is perpendicular to wire 2, as shown in Figure If the field set up at G G G G wire 1 by wire 2 is calculated, the force F12 acting on wire 1 is found to be equal in magnitude G and opposite in direction to F Hence, we find that parallel straight conductors carrying currents in the same direction attract each other, and parallel straight conductors carrying currents in opposite directions repel each other.

Figure 59a shows how this effect can be demonstrated in the classroom. Several compass needles are placed in a horizontal plane near a long vertical wire. These observations demonstrate that the direction of the magnetic field produced by the current in the wire is consistent with the right-hand rule described in Figure Because the compass G G needles point in the direction of B , we conclude that the lines of B form circles around the G wire, as discussed in the preceding section.

By symmetry, the magnitude of B is the same everywhere on a circular path centered on the wire and lying in a plane perpendicular to the wire. Along this path, the vectors d s and B are parallel at each point see Fig. Furthermore, the magnitude B is constant on this circle and is given by G G equation Therefore, the sum of the products B. Although this result was calculated for the special case of a circular path surrounding a wire, it holds for a closed path of any shape surrounding a current that exists in an unbroken circuit.

The direction of the magnetic field is perpendicular to the wire and is in the direction the fingers of your right hand would curl if you wrapped them around the wire with your thumb in the direction of the current see Figure It is also inversely proportional to the distance from the wire, as given by equation The expression for the magnitude magnetic field vector is interest to the wire. Such coils, called solenoids, have an enormous number of practical applications.

The field can be greatly strengthened by the addition of an iron core. Such cores are typical in electromagnets. The expression is an idealization to an infinite length solenoid, but provides a good approximation to the field of a long solenoid. The field is essentially perpendicular to the sides of the path, giving negligible contribution.

If the end is taken so far from the coil that the field is negligible, then the length inside the coil is the dominant contribution. Figure Magnetic field created by a long straight coil of wire solenoid carrying an electric current. The device consists of a conducting wire wrapped around a ring a torus made of a nonconducting material.

For a toroid having N closely spaced turns of wire, we calculate the magnetic field in the region occupied by the torus, a distance r from the center. By symmetry, we see that the magnitude of the field is constant on this circle and tangent to G G it, so B. Furthermore, note that the circular closed path surrounds N loops of wire, each of which carries a current I.

However, if r is very large compared with the cross-sectional radius of the torus, then the field is approximately uniform inside the torus. The current enclosed by the dashed line is just the number of loops times the current in each loop.

Figure Magnetic field created by a toroid carrying an electric current. The vector field B is G G G known among electrical engineers as magnetic flux density or magnetic induction, or simply G magnetic field, as used by physicists. The vector field H is known among electrical engineers as the magnetic field intensity or magnetic field strength and is also known among physicists as auxiliary magnetic field or magnetizing field.

However, when the generated fields pass through magnetic materials which themselves contribute internal magnetic fields, ambiguities can arise about what part of the field comes from the external currents and what comes from the material itself. It has been common practice to define another magnetic field quantity, usually called the G "magnetic field strength" and designated by H.

More generally, magnetic flux is defined by a scalar product of the magnetic field vector and the area element vector. The SI unit of magnetic flux is the weber Wb. This is the net number, i. If we approach the loop with a permanent magnet, we see a current being registered by the galvanometer. The results can be summarized as follows: i.

A current appears only if there is relative motion between the magnet and the loop. Faster motion results in a larger current intensity. If we reverse the direction of motion or the polarity of the magnet, the current reverses sign and flows in the opposite direction.

When the current in loop 1 is constant, no induced current is observed in loop 2. An emf is induced in a loop when the number of magnetic field lines or magnetic flux that pass through the loop is changing. This law is actually a consequence of the law of conservation of energy. The direction of the flow of induced current in a loop is accurately predicted by what is known as Lenz's law or Lenz's rule.

In the figure we show a bar magnet approaching a loop. The induced current flows in the direction indicated because this current generates an induced magnetic field that has the field lines pointing from left to right. The loop is then equivalent to a magnet whose north pole faces the corresponding north pole of the bar magnet that is approaching the loop.

The loop then repels the approaching magnet and thus opposes the change in the original magnetic flux that generated the induced current. Example: A coil consists of turns of wire having a total resistance of 2. Each turn is a square of side 18 cm, and a uniform magnetic field directed perpendicular to the plane of the coil is turned on. If the field changes linearly from 0 to 0. In this section we describe what is called motional electromotive force, which is the emf induced in a straight conductor moving through a constant magnetic field.

Part of the loop is located in a region where a uniform magnetic field exists. This flux decreases with time; according to constant speed v. Using Faraday's law we can determine the resulting emf known as Figure Depicting the Physic 1 Module 4: Electricity and magnetism 23 self-induction. Example: a Calculate the inductance of an air-core solenoid containing turns if the length of the solenoid is Magnetic energy 1.

When the switch S is closed, the current immediately starts to increase. The induced emf or back emf in the inductor is large, as the current is changing rapidly. As time goes on, the current increases more slowly, and the potential difference across the Figure A series RL circuit. In inductors, energy is similarly stored, only now in the magnetic field.

Just as with capacitors, where the electric field is created by a charge on the capacitor and electric energy is stored inside the capacitors, we now have a magnetic field created when there is a current through the inductor. Thus, just as with the capacitors, the magnetic energy is stored inside the inductor. From equation , we see that magnetic energy density is proportional to the square of the square of the field magnitude.

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