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Constant Current

EXACT Magnetic Effects Of Current

Magnetic Effects Of Current

The term "magnetic effects of current" means that" a current flowing in a wire produces a magnetic field round it ". The magnetic effect of current was discovered by Oersted found that a wire carrying a current was able to deflect a magnetic needle. It concludes that a current flowing in a wire always gives rise to a magnetic field round it, the , telephone and radio, all utilize the magnetic effect of current.

From at least the eighteenth century, people were trying to determine the connection between electricity and magnetism. Benjamin Franklin tried to magnetize a needle by electrical discharge. Sir Edmund Whittaker in the classical treatise History of the Theories of Aether and Electricity writes: "In 1774 the Electoral Academy of Bavaria proposed the question, `Is there a real and physical analogy between electric and magnetic forces?' as the subject of a prize." In 1805, two French investigators attempted to determine whether a freely suspended voltaic pile orients itself in any fixed direction relative to the earth. In 1807, Hans Christian Oersted (1777 - 1851), professor of natural philosophy at the University of Copenhagen, announced his intention to investigate the effects of electricity on the magnetic compass needle. Oersted's intention did not bear fruit for some time, but in July 1820 he published a pamphlet describing the results of experiments that "were set on foot in the classes for electricity, galvanism, and magnetism, which were held by me in the winter just past."

In these experiments, Oersted showed that a magnetic compass needle is subjected to a systematic pattern of forces in the presence of a wire closing a voltaic circuit and carrying an electric current. Note, we use the convention in which electric current flows from the positive terminal to the negative terminal through the wire. [demo Oersted's experiment: undisturbed needle; wire above; wire below; vertical wire current coming and going]

Following Oersted's discovery, it was immediately surmised that the magnetic effect of the current should induce magnetism in pieces of iron just as is done by an ordinary magnet, and this was quickly verified.

Magnetic Lines of Force

The direction of the magnetic field due to a current may be studied by drawing the magnetic lines of force. A vertical wire AB is passed through a horizontal cardboard PQRS. Ion filings are sprinkled on the cardboard. Current is passed through it by connecting a battery to it. Iron filings spread evenly on the cardboard. When a compass needle is placed on the cardboard, the direction of the needle will show the direction of the magnetic field. The point on the cardboard where the north pole of the needle is siturated is marked. The needle is shifted a little so that its south pole takes the same position where the north pole was situated previously. The position of the north pole is marked. If the current is strong the lines will be circular. The arrows on the circular lines show the direction of the magnetic field.

Magnetic Field Lines Due to Straight Wire

If the direction of the current is reversed, the lines will still be circular, but the directions of the lines will be reversed, which can be verified using the compass needle.

Magnetic Field

A magnetic field is defined as a region in which a magnetic force is present. In a magnetic field, the magnetic dipole (two equal and oppositely charged or magnetized poles separated by a distance) experiences a turning force, which tends to align it parallel to the direction of the field. The concept of a magnetic field can be understood with the help of the following activity:

Place a piece of cardboard over a magnet

Sprinkle some iron filings onto the cardboard

Tap the cardboard gently and draw what you see

The iron filings show the magnetic field of the magnet

Maxwell's Right Hand Grip Rule

The direction of the magnetic field around a current carrying conductor can be explained by a simple rule known as Maxwell's right hand grip rule. If we hold the current carrying wire in our right hand in such a way that the thumb is stretched along the direction of the current, then the curled fingers give the direction of the magnetic field produced by the current.

Maxwell's Right Hand Grip Rule

Magnetic Field due to a Solenoid

When a long wire is coiled in the shape of a spring so that the turns are closely spaced and insulated from each other it forms a solenoid. Generally, a wire is coiled over a non-conducting hollow cylindrical tube. An iron rod is often inserted inside the hollow tube. This rod is called the core.

Magnetic Field due to a Solenoid

The free ends of the solenoid are connected to a battery to pass current through the solenoid. This produces a magnetic field. The magnetic field inside the coil is almost constant in magnitude and direction. The current carrying solenoid produces magnetic field similar to that of a bar magnet. One end of the solenoid becomes the north pole and the other end becomes a south pole.

The magnitude of the field depends on the following factors. The magnetic field is directly proportional to:

the amount of current passing through the solenoid

the number of turns of the solenoid. It also depends on the core material.

Since the magnetic field formed by the solenoid is temporary it is used to make electromagnets. Electromagnets are used in electric bells, cranes, etc.

Magnetic flux density

The magnetic flux density can be thought of as the concentration of field lines. We can increase the force by increasing any of the terms within the equation. If we coil up the wire, we increase its length within the magnetic field.

If we look at the magnetic field of a solenoid, we know that it is like a bar magnet:

We can see that the magnetic field strength is uniform within the solenoid. However the flux density becomes less at the ends, as the field lines get spread out.

We need a term that tells us the number of field lines, and it is called the magnetic flux. It is given the physics code  (‘Phi', a Greek capital letter ‘Ph'), and has the units Weber (Wb). The formal definition is:

The product between the magnetic flux density and the area when the field is at right angles to the area.

In code we write:

F = BA

Remember that flux density is the number of field line per unit area, not unit volume!

The flux linkage is the flux multiplied by the number of turns of wire. If each turn cuts (or links) flux F, the total flux linkage for N turns must be NF. We can also write this as NBA. In other words:

Flux linkage = number of turns of wire ´ magnetic field strength ´ area

Magnetic linkage

To investigate the links between the solar surface and corona and the fine-scale structure of the Sun's magnetized atmosphere on all scales requires the combined observations of VIM and EUI, together with observations of EUS exploring the energetics and dynamics through spectroscopy. The Solar Orbiter mission is needed to do this science because it offers a unique suite of capable instruments and unparalleled set of vantage points at high latitudes and in partial co-rotation.

These conditions will allow us to make high-resolution observations of the vector magnetic field together with plasma emission in the transition region and lower corona, which can not be done on any other ongoing or planned solar space mission. To establish the magnetic linkage, as well as its change by field line reconnection, between the photosphere, transition region and corona for various magnetic structures is a key objective.

It is already known from SOHO and TRACE observations that the main layer to be observed is the magnetic transition region (MTR, reaching up to about 10 Mm) that consists of small cool loops and tenuous funnels at temperatures of up to several 105 K. Below about 5 Mm the MTR is highly dynamic at scales of one second of arc and below (150 km pixel size of Solar Orbiter is ideal). As numerical simulations have shown, it is from the chromosphere to the middle MTR where reconnection (jets, explosive events) mostly take place as the result of magneto convection in the photosphere.

EUS instrument requirements

1. Emission line requirements

To diagnose adequately the MTR a long-wavelength channel is indispensable, which should contain reference lines at rest in the chromosphere for Doppler shift calibration and for co-alignment with the VIM context-magnetograms by means of pattern recognition, and which must provide a broad coverage in temperature from about 5 103 K to about 5 105 K (line ratios for density diagnostic desirable).

2. Spectral and spatial resolution requirements

We need to resolve the lines not only for intensity measurements, but their profiles need to be resolved in order to study the line widths and shift (flows and heating). There is a whole zoo of possible structures in the MTR which should be observed. Typically, for synergy the field of view of the EUI HRI should be covered. Special observations of an individual funnel, a bright point or granule, for example, would only require, say, a 3 × 3 arcsec2 field of view. Fast scanning capability of the spectrometer is essential for the study of dynamics.

3. Time resolution (incl. count rates)

Short exposure times (of order seconds) are needed to follow fast reconnection and quick topological changes of the field and the resulting variations in VUV emission in the lower TR.

Expression for the Force on moving charges particle in a magnetic field

Force on a charged particle

A charged particle moving in a B-field experiences a sideways force that is proportional to the strength of the magnetic field, the component of the velocity that is perpendicular to the magnetic field and the charge of the particle. This force is known as the Lorentz force, and is given by

where F is the force, q is the electric charge of the particle, v is the instantaneous velocity of the particle, and B is the magnetic field (in teslas).

The Lorentz force is always perpendicular to both the velocity of the particle and the magnetic field that created it. When a charged particle moves in a static magnetic field it will trace out a helical path in which the helix axis is parallel to the magnetic field and in which the speed of the particle will remain constant. No work will be done in this particular case scenario.

Force on current-carrying wire

Main article: Laplace force

The force on a current carrying wire is similar to that of a moving charge as expected since a charge carrying wire is a collection of moving charges. A current carrying wire feels a sideways force in the presence of a magnetic field. The Lorentz force on a macroscopic current is often referred to as the Laplace force. Consider a conductor of length l and area of cross section A and has charge q which is due to electric current i .If a conductor is placed in a magnetic field of induction B which makes an angle θ (theta) with the velocity of charges in the conductor which has i current flowing in it. then force exerted due to small particle q is F = qvBsinθ then for n number of charges it has N = nlA then force exered on the body is f=FN =>f=(qvBsinθ)(nlA) but nqvA = i that is f =Bilsinθ

Direction of force

The direction of force on a charge or a current can be determined by a mnemonic known as the right-hand rule. Using the right hand and pointing the thumb in the direction of the moving positive charge or positive current and the fingers in the direction of the magnetic field the resulting force on the charge points outwards from the palm. The force on a negatively charged particle is in the opposite direction. If both the speed and the charge are reversed then the direction of the force remains the same. For that reason a magnetic field measurement (by itself) cannot distinguish whether there is a positive charge moving to the right or a negative charge moving to the left. (Both of these cases produce the same current.)

The Cyclotron

The largest particle accelerators have dimensions measured in miles. A cyclotron is a particle accelerator that is so compact that a small one could actually fit in your pocket. It makes use of electric and magnetic fields in a clever way to accelerate a charge in a small space.

A cyclotron consists of two D-shaped regions known as dees. In each dee there is a magnetic field perpendicular to the plane of the page. In the gap separating the dees, there is a uniform electric field pointing from one dee to the other. When a charge is released from rest in the gap it is accelerated by the electric field and carried into one of the dees. The magnetic field in the dee causes the charge to follow a half-circle that carries it back to the gap.

While the charge is in the dee the electric field in the gap is reversed, so the charge is once again accelerated across the gap. The cycle continues with the magnetic field in the dees continually bringing the charge back to the gap. Every time the charge crosses the gap it picks up speed. This causes the half-circles in the dees to increase in radius, and eventually the charge emerges from the cyclotron at high speed.