What is the average induced current

A wire loop of radius 0. The field changes to The plus and minus signs here refer to opposite directions through the loop. Find the magnitude of the average induced emf in the loop during this time.

The flexible loop in Figure P The loop is grasped at points A and B and stretched until it closes. If it takes 0. This is a case where the change in flux is caused by a change in the area of the loop.

Both the magnetic field and the angle q remain constant. When the loop is stretched so that its area is zero, the flux through the loop is zero. An interesting application of Faraday's law is to produce an emf via motion of the conductor. As a simple example, let's consider a conducting bar moving perpendicular to a uniform magnetic field with constant velocity v. This force will act on free charges in the conductor. It will tend to move negative charge to one end, and leave the other end of the bar with a net positive charge.

The separated charges will create an electric field which will tend to pull the charges back together. If the direction of motion is reversed, so is the polarity of the potential difference.

Now let's consider what happens when we add conducting rails for the top and bottom of the bar to contact, and a resistor between the rails to complete a loop. We can apply Faraday's law to the complete loop. This is the same result we obtained considering the conducting bar by itself.

Over a region where the vertical component of the Earth's magnetic field is Similar principles apply to computer hard drives, except at a much faster rate.

Here recordings are on a coated, spinning disk. Read heads historically were made to work on the principle of induction. Today, most hard drive readout devices do not work on the principle of induction, but use a technique known as giant magnetoresistance. The discovery that weak changes in a magnetic field in a thin film of iron and chromium could bring about much larger changes in electrical resistance was one of the first large successes of nanotechnology.

Another application of induction is found on the magnetic stripe on the back of your personal credit card as used at the grocery store or the ATM machine. This works on the same principle as the audio or video tape mentioned in the last paragraph in which a head reads personal information from your card.

Another application of electromagnetic induction is when electrical signals need to be transmitted across a barrier. Consider the cochlear implant shown below. Sound is picked up by a microphone on the outside of the skull and is used to set up a varying magnetic field. A current is induced in a receiver secured in the bone beneath the skin and transmitted to electrodes in the inner ear. Electromagnetic induction can be used in other instances where electric signals need to be conveyed across various media.

Figure 3. Electromagnetic induction used in transmitting electric currents across mediums. Another contemporary area of research in which electromagnetic induction is being successfully implemented and with substantial potential is transcranial magnetic simulation. A host of disorders, including depression and hallucinations can be traced to irregular localized electrical activity in the brain. 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?