Purpose

In this experiment, you will gain an understanding of electromagnetic induction as expressed in terms of Faraday’s law. You will also predict and test how changes in a magnetic field affect an electric field.

The discovery that a moving charge or current generated a magnetic field came as a big surprise to scientists. What may have been an even bigger surprise is that the reverse is true. A magnetic field can induce an electric field that can induce a current (moving charge). The relationship between electric current and magnetic field has a wide range of technological applications— from electric motors to electric door locks.

Michael Faraday was the first to observe the relationship between magnetic fields and a generated current. In one of Faraday’s basic science experiments he connected a loop of conducting wire to an ammeter, a device used to measure electric current on circuits without a battery. Without a battery, there was no current in the wire. However, when a bar magnet was moved toward the loop, there was a current reading on the ammeter. As soon as the bar magnet stopped moving toward the loop, the reading returned to zero amps. When the bar magnet was then pulled away from the loop, the current reading on the ammeter came back, but the current was now in the opposite direction. Faraday realized if there is a current in the wire, there must be a voltage somewhere too. From this and a few other simple experiments, Faraday discovered that changing the amount of magnetic field lines passing through a loop induces a voltage in that loop.

In order to apply Faraday’s Law, the number of magnetic field lines that pass through a loop needs to be calculated. The number of magnetic field lines that pass through an area (in this case, a loop of conducting wire) is called magnetic flux. Consider Figure 1 in which a loop is enclosing an area, A, and it is in a magnetic field, B.

Figure 1: Magnetic field lines (blue arrows) flowing through the area of a loop (gray circle)

Remember, it is the change in the magnetic flux that induces a voltage in the loop. This voltage has a special name called induced electromotive force or induced emf (ε). The magnitude of the induced emf in a loop is equal to the rate at which the magnetic flux, dΦ, is changing over time, dt, multiplied by the number of turns or loops in the coil, N. Since induced emf opposes the change in magnetic flux, the rate is expressed as negative:

Faraday’s Law of Induction

ε =?N ddt?

If the flux changes at a steady rate the induced emf is:

ε =?N ddt? =?NΔΔ?t

A second right-hand rule (Figure 2) describes the force on a charged particle moving through a uniform magnetic field that points in one direction. If you point your index finger in the direction of the moving charge with the face of your palm (or middle finger) in the direction of the magnetic field, then your thumb will point in the direction of the force on a positively charged particle (for negative charges, the force is in the opposite direction). If, instead of one charged particle, there is current traveling through a conductor (such as a length of wire), then the same rule relates the directions of the current, the magnetic field and the force on the current-carrying object.

Figure 2: The series of gray X’s represent a uniform magnetic field in a direction pointing into the page. Given the direction of the charge as indicated by arrows, the force on the segment of wire is in the upward direction.

In general, the force on a moving charge, F, is equal to the product of the magnitude of the moving charge, q, its velocity, v, and the magnetic field strength in a direction perpendicular to the velocity, B:

F = qvBsin(θ)

The force will point in the direction indicated by the right hand rule for magnetic force. If instead of one moving charge there is an electric current, the force is a product of the current, I, flowing through a wire section of length, L, and the magnetic field strength direction perpendicular to the current, B:

F = ILB

In cases where the angle between the current and the field is not 90^?, only the vertical component of the magnetic field is considered.

One of the most useful inventions within the last 150 years is the electric motor (Figure 3), which takes advantage of the relationship between electric current and magnetic field. An electric motor consists of a coil of wire (called the armature) situated within a magnetic field (created by either permanent magnets or electromagnets). When electric current passes through the coil, the parts of the coil perpendicular to the field experience a force that rotates the armature. If the current is engineered to reverse at just the right moment, the armature will continue to rotate, drive a shaft, and turn electric current into mechanical work.

Magnetic Force

Figure 3: A side view (left) and top view (right) of a motor armature rotating between two magnets (gray). A circle with a cross signifies a direction into the page, and a circle with a dot represents a direction out of the page. When viewed from above with current traveling in the clockwise direction, an upward force is experienced by the right side, and a downward force on the left side. These forces create a torque that turns the armature in a counterclockwise direction (shown in left figure). Once the armature reaches the vertical position the current must be reversed to prevent it from getting stuck.

A generator uses similar principles as the motor, but the process is reversed: mechanical work is converted into electrical energy. According to the right-hand rule, when a coil of wire is forced to rotate within a magnetic field, a current in the wire will be induced. For example, if you were to manually rotate the armature in Figure 3, a current would be induced in the wires in a direction that would alternate every half turn. For this reason, generators that produce alternating current (AC) are fairly simple to build.

Transformers (Figure 4) convert high voltages to low voltages by utilizing changing magnetic fields and currents. Without a transformer, the circuits in simple home appliances would have to be built to withstand the high voltage electricity that the electric company sends to houses. Transformers are used in almost every electronic device that plugs into a wall socket.

Figure 4: The change in voltage over this simple transformer depends on the number of turns of wire around each side. The total magnetic field flow, called magnetic flux, is the same through each set of coils, but the larger number of turns on the right makes V2 proportionally larger than V1. Imagine the wires on the left as coming from the electric company, and those on the right as feeding into long-distance power lines.

1. Analyze Graph 1and rank the change in magnetic flux during Times A, B, C, D, and E from at least to greatest. Use an equal sign to designate equal magnetic fluxes.

 D<C=E<A=B

2. A MRI technician neglected to remove a metal bracelet from a patient. The bracelet is 7.0 cm in diameter. If the magnetic field is oriented from the patient’s foot to head, the area of the bracelet will be perpendicular to the magnetic field. During the scan, the magnetic field increases from 0 T to 1 T in 1.5 seconds. What is the magnitude of the induced emf in the bracelet? Show your work.

Emf induced = -N

                        = -(1)= -2.566 mV

Magnitude of emf induced in the bracelet = 2.566 mV

3. A wire loop is being pulled out of a uniform magnetic field directed into the page at a constant speed, v (Figure 5). Draw the direction of the force on the wire due to the magnetic field if the

 Current in the loop is going in the clockwise direction.

According to Lenz law, the direction of induced current is such that it always opposes the change in magnetic flux. In other words, a change in magnetic flux is always opposed. As the wire is moving towards right, the magnetic flux decreases. The induced current will try to  stop(minimize) this motion, and hence, the direction of Force acting on the wire by the magnetic field is towards left.

Figure 6:

shows a conductor moving in a uniform magnetic field. Show that when the conductor moves in the magnetic field, the magnetic force induces an electric field in the conductor by drawing what occurs inside of the conductor. Explain your drawing. Hint: Think about the magnetic force on the charges inside the conductor.

A conductor consists of free electrons and can move freely inside the conductor when the conductor is moving in a magnetic field

region with constant velocity. As the conductor moves right, the electrons fill experience a magnetic force towards downward and

and will start to accumulate in the lower part of it. As a result, positive charge(deficiency of electrons) starts to accumulate at the

upper part of the conductor. Due to this separation of charges within the conductor, an electric field is generated acting

downwards due to this charge accumulation as shown below :