What is the significance of the negative sign with magnetic field

Now consider imaginary the loop c that is located inside the solenoid. We have shown above that the field is pointing upwards inside the solenoid, so the horizontal portions of loop c doesn't contribute anything to the integral. Thus the integral of the up side 1 is equal to the integral of the down side 2. Since we can arbitrarily change the dimensions of the loop and get the same result, the only physical explanation is that the integrands are actually equal, that is, the magnetic field inside the solenoid is radially uniform.

Note, though, that nothing prohibits it from varying longitudinally which in fact it does. A similar argument can be applied to the loop a to conclude that the field outside the solenoid is radially uniform or constant. This last result, which holds strictly true only near the centre of the solenoid where the field lines are parallel to its length, is important inasmuch as it shows that the field outside is practically zero since the radii of the field outside the solenoid will tend to infinity.

An intuitive argument can also be used to show that the field outside the solenoid is actually zero. Magnetic field lines only exist as loops, they cannot diverge from or converge to a point like electric field lines can see Gauss's law for magnetism. The magnetic field lines follow the longitudinal path of the solenoid inside, so they must go in the opposite direction outside of the solenoid so that the lines can form a loop. However, the volume outside the solenoid is much greater than the volume inside, so the density of magnetic field lines outside is greatly reduced.

Now recall that the field outside is constant. In order for the total number of field lines to be conserved, the field outside must go to zero as the solenoid gets longer.

Now we can consider the imaginary loop b. Take the line integral of B around the loop, with the length of the loop l. This equation is for a solenoid with no core. The inclusion of a ferromagnetic core, such as iron , increases the magnitude of the magnetic field in the solenoid.

In transcranial magnetic stimulation , a rapidly varying and very localized magnetic field is placed close to certain sites identified in the brain. Weak electric currents are induced in the identified sites and can result in recovery of electrical functioning in the brain tissue.

In such individuals, breath can stop repeatedly during their sleep. A cessation of more than 20 seconds can be very dangerous. Stroke, heart failure, and tiredness are just some of the possible consequences for a person having sleep apnea. The concern in infants is the stopping of breath for these longer times.

One type of monitor to alert parents when a child is not breathing uses electromagnetic induction. A pickup coil located nearby has an alternating current induced in it due to the changing magnetic field of the initial wire. If the child stops breathing, there will be a change in the induced current, and so a parent can be alerted. Calculate the magnitude of the induced emf when the magnet in Figure 1 a is thrust into the coil, given the following information: the single loop coil has a radius of 6.

Since the area of the loop is fixed, we see that. While this is an easily measured voltage, it is certainly not large enough for most practical applications. More loops in the coil, a stronger magnet, and faster movement make induction the practical source of voltages that it is. If emf is induced in a coil, N is its number of turns. Conceptual Questions A person who works with large magnets sometimes places her head inside a strong field. She reports feeling dizzy as she quickly turns her head.

How might this be associated with induction? A particle accelerator sends high-velocity charged particles down an evacuated pipe. Explain how a coil of wire wrapped around the pipe could detect the passage of individual particles. Sketch a graph of the voltage output of the coil as a single particle passes through it. Referring to Figure 5 a , what is the direction of the current induced in coil 2: a If the current in coil 1 increases? Figure 5. Referring to Figure 5 b , what is the direction of the current induced in the coil: a If the current in the wire increases?

Referring to Figure 6, what are the directions of the currents in coils 1, 2, and 3 assume that the coils are lying in the plane of the circuit : a When the switch is first closed? Suppose a turn coil lies in the plane of the page in a uniform magnetic field that is directed into the page. The coil originally has an area of 0.

It is stretched to have no area in 0. What is the direction and magnitude of the induced emf if the uniform magnetic field has a strength of 1. Find the average emf induced in his wedding ring, given its diameter is 2. Integrated Concepts Referring to the situation in the previous problem: a What current is induced in the ring if its resistance is0. An emf is induced by rotating a turn, Find the magnetic field strength needed to induce an average emf of 10, V.

Integrated Concepts Approximately how does the emf induced in the loop in Figure 5 b depend on the distance of the center of the loop from the wire? Integrated Concepts a A lightning bolt produces a rapidly varying magnetic field. If the bolt strikes the earth vertically and acts like a current in a long straight wire, it will induce a voltage in a loop aligned like that in Figure 5 b.

What voltage is induced in a 1. The heat transferred will be 2. This is not a significant amount of heat. Skip to main content.

Search for:. Determine the direction of the magnetic field B. Determine whether the flux is increasing or decreasing. Now determine the direction of the induced magnetic field B. It opposes the change in flux by adding or subtracting from the original field.

Use RHR-2 to determine the direction of the induced current I that is responsible for the induced magnetic field B. The direction or polarity of the induced emf will now drive a current in this direction and can be represented as current emerging from the positive terminal of the emf and returning to its negative terminal.

For practice, apply these steps to the situations shown in Figure 1 and to others that are part of the following text material. Applications of Electromagnetic Induction. The induced emf produces a current that opposes the change in flux, because a change in flux means a change in energy.