## SAT Physics Magnetism - Permanent Or Fixed Magnets

PERMANENT OR FIXED MAGNETS
Fixed magnets are the traditional magnets with which people are familiar. They include bar magnets and horseshoe magnets. Their magnetic properties are the result of electron spin in the orbitals of the magnet’s atoms. Although the fixed magnet does not appear to be moving, in fact, the motion of the spinning electrons causes the magnetic field. In most substances, the net spin of all the electrons cancels. In some substances, such as iron, the net effect of the spinning electrons does not cancel. So each atom acts like a tiny magnet. Groups of atoms having a similar magnetic orientation are known as domains. When all the domains of a magnetic substance are aligned, the substance becomes a fixed magnet with a set magnetic field.
The magnetic fields around and between fixed magnets have known properties. The magnetic field surrounding a fixed magnet appears similar to the electric field between an electron and a proton, as shown in Figure 13.1. Figure 13.1. Magnetic and electric field lines

Fixed magnets have a north pole and a south pole. These poles are analogous to positive and negative aspects of an electric field, but they are not the same thing. Figure 13.1 shows only the magnetic field outside of a fixed magnet, which appears to extend from north to south just as the electric field extends from positive to negative. The electric field terminates on charges. However, the magnetic field forms continuous closed loops. The field lines in the diagram actually extend into and through the fixed magnet. Inside the magnet, the lines run from south to north. However, we are most concerned with the lines outside of fixed magnets as this portion of the field interacts with other magnets. Fixed magnets can be used to cre­ate uniform magnetic fields, as shown in Figure 13.2. The letter B represents the vector for magnetic field, which is measured in teslas (T). Figure 13.2. Uniform magnetic fields

In many problems, the magnets are not drawn. Only the magnetic field is given or its direction is stated. Quite often, the magnets cannot be drawn as they are not in the plane of the page. The uniform magnetic fields shown in Figure 13.3 are oriented in the z-direction. The magnets that created them are located in front of and behind the plane of this page. Dots are used to indicate a field coming out of the page and X’s are used to indicate a field going into the page. Figure 13.3. Uniform magnetic fields in the z-direction

The even spacing of the symbols representing the field lines indicates that the magnetic fields are uniform. They have the same magnitude and direction at every point.

CURRENT-CARRYING WIRES
The magnetism of a current-carrying wire is essentially the sum of the magnetism of the moving charges that comprise the current in the wire.

Visualizing the Field of Current-Carrying Wires
A wire is essentially a long cylinder. The magnetic field surrounding a current-carrying wire forms concentric circles around every part of the wire. Figure 13.4(a) shows a representation of the circling field. Figure 13.4(b) shows how this field can be rendered two-dimensionally. Figure 13.4. Magnetic fields around a current-carrying wire

Figure 13.4(b) may seem confusing since it shows only a slice of the magnetic field passing through the plane of the page. Above the wire, the field is shown coming out of the page. Below the wire, it is shown entering the page. The direction of the field above and below the wire is determined by the right-hand rule. The thumb of the right hand points in the direction of the current. The curled fingers point in the direction of the circular magnetic field created by the current. When the hand is oriented with the fingers above the wire, the tips of the fingers point out of the page in the +z-direction. The field is represented by dots. When the hand is oriented with the fingers below the wire, the tips of the fingers point into the page in the -z-direction, and the field is represented by X’s. What the field is doing in front of the wire and behind the wire cannot be shown in the plane of the page.
The diagrams in Figure 13.4 can be rotated 90 degrees so that the wire and its current appear to be coming out of or going into the page as shown in Figure 13.5. This diagram clearly shows the circling magnetic fields. Again, the right-hand rule can be used to deter-mine the direction the field is circling. In the left diagram, point the right thumb into the page (X) and the fingers will curl clockwise. In the right diagram, point the right thumb out of the page (dot) and the fingers will curl counterclockwise Figure 13.5. Using the right-hand rule to determine the direction of the magnetic field
Problems most often ask for the direction of the field at a specific point, as shown in Example 13.1.

Direction of the Magnetic Field Around a Wire The diagrams above show two current-carrying wires. The wire on the left is in the plane of the page and carries a current in the +x-direction. The wire on the right is perpendicular to the page and carries a current in the +z-direction. Determine the direction of the magnetic field at points C and D.

WHAT'S THE TRICK?

Use the right-hand rule. Even though the field is circling the wire, the direction of the field at a single point is an instantaneous value. It will be tangent to the circling field at that point.
Point C: Out of the page, +z-direction.
Point D: Up, +y-direction

Magnitude of the Magnetic Field of a Wire
The magnitude of the magnetic field, B, of a long, straight, current-carrying wire is solved with the following equation. The constant, μ0, is known as the permeability of free space. It has the value μ0 = 4π × 10-7 T • m/A. The current in the wire is represented by I and is measured in amperes. The dis­tance, r, is measuredfrom the center of the wire to the point where the field is to be solved.
The magnetic field is directly proportional to the current in the wire and inversely propor­tional to the distance from the wire

Magnetic Field Due to a Current
A long, straight wire carries a current of 2.0 amperes. Determine the magnitude of the magnetic field at a point 10 centimeters from the wire.

WHAT'S THE TRICK?

Use the formula for long, straight wires. Always convert to acceptable units: from centimeters to meters. FORCE ON MOVING CHARGES
Uniform Magnetic Fields and Moving Charges

Tiny moving charges such as protons and electrons interact with magnetic fields. These mov­ing charges are so small that the magnetic fields surrounding them are negligible. However, when moving charges move perpendicularly to external magnetic fields created by larger magnets, such as fixed magnets and current-carrying wires, the moving charges experience a force of magnetism. The following formula calculates the magnetic force on a charge moving in an external magnetic field The force of magnetism on a moving charge is the product of its charge (q), its velocity ,and the magnetic field , through which it is moving. The formula contains sin θ,where θ is the angle between the velocity and the magnetic field vectors. The value of sin θ is at its maximum and equal to 1 when θ - 90°. Therefore, to receive a maximum force of magnetism, charges must move perpendicularly to the magnetic field. Most exam problems requiring the formula will send charges perpendicularly to the magnetic field and will solve only for vector magnitude. As a result, the formula often simplifies to the following.
Fb = qvB
All three vector quantities, FB, , and , in the above formula must be perpendicular to one another. They each lie on separate axes and require analysis in all the three dimensions (x, y, and z). This means that a charge moving parallel to the field will experience no magnetic forces at all. When charges move parallel to the magnetic field, θ = 90° and the magnetic force is zero. Zero quantities are often tricky conceptual questions. When charges move parallel to magnetic fields, they are subject to inertia because there is no force of magnetism. If the charges are stationary, they remain stationary. If they are moving at constant velocity, they continue moving at constant velocity.
Electric and gravity fields can cause objects to change speed and/or direction. Magnetic force acting on moving charges is centripetal, resulting in uniform circular motion. Charges moving in magnetic fields are accelerating, but they have constant speed. Figure 13.6 and Table 13.2 compare and contrast the three major uniform fields, the forces they create, and the motion they cause. Figure 13.6 Three major uniform fields

Table 13.2 Forces and Motion Caused by Various Uniform Fields The circular motion of moving charges is easier to visualize if the magnetic field is rotated so that it is oriented in the direction (out of or into the page) as shown in Figure 13.7. Figure 13.7. The magnetic field rotated in the z-direction

Only positive charges are shown in Figure 13.7. If negative charges were shown, they would circle in the opposite direction. The direction, whether clockwise or counterclockwise, that a charge will circle is determined by a slightly different version of the right-hand rule. This version of the right-hand rule is for determining the direction of force on a moving, charged particle by a magnetic field. The previous version of the rule was used to determine the direc­tion of a magnetic field created by the current in a long, straight wire. When magnetic force is involved, the fingers are not curled and should be extended straight, with the thumb and fingers separated by 90° as shown in Figure 13.8. Figure 13.8. Using the right-hand rule with magnetic force

To find the direction of force, point the thumb in the direction of the velocity, v, of the moving charge. Point the extended fingers in the direction of the magnetic field lines. The direction that the palm of the hand pushes (a force is a push) is the direction of the force of magnetism. Note that on the left side of Figure 13.8, the palm is pushing out of the page, and the force of magnetism shown is in the positive z-direction.
The right-hand rule gives the direction of force, which can be used to determine whether the object will circle clockwise or counterclockwise. When charges move in a magnetic field the only force acting on them is the force of magnetism. This force causes uniform circular motion since the magnetic force acts perpendicularly to motion. Therefore, the force of magnetism must point toward the center of the circle. In the left diagram in Figure 13.7, the force of magnetism points downward. Thus, the center of the circle must be below the point where the charge enters the field. The charge must circle clockwise. The opposite is true for the charge entering the -z field in the right diagram in Figure 13.7.
Negative (opposite) charges will always move in a direction opposite that of positive charges. If a positive charge circles clockwise, a negative charge circles counterclockwise. You can handle negative charges in one of two ways.
1. Use the right-hand rule and give the opposite answer.
2. Use the left hand for negative charges.
Charges Moving in Uniform Magnetic Fields A charge, q, moving at a speed of v enters a uniform magnetic field, B, as shown in the diagram above.
(A) Determine the radius of the circular path in terms of the given variables.

WHAT'S THE TRICK?

In circular motion, force centripetal (Fc) is used instead of The force causing the circular motion and pointing toward the center of the circle is the force of magnetism, FB.
FC = FB (B) Determine whether the charge shown in the diagram is positive or negative.

WHAT'S THE TRICK?

The center of the clockwise circular motion is below the point where the charge enters the field. The palm of the hand must be oriented downward to push toward the center. Only the left hand is capable of aligning with all three vectors: v, B, and FB. Therefore, the charge is negative.

Work Done by the Magnetic Force
The force of magnetism does no work on moving charges. The force of magnetism always acts perpendicularly to the motion of charges. In order to do work, a force must be parallel to an object’s motion. Since no work is done, the force of magnetism cannot change the kinetic energy and velocity of an object. However, the perpendicular force of magnetism can change the direction of moving charges, causing them to circle at constant speed.

Current-Carrying Wires and Moving Charges
A charge may also be moving through the magnetic field created by a current-carrying wire. The equation for the magnitude of the force of magnetism acting on a charge near a current-carrying wire is the same as when a charge moves in a uniform magnetic field. Although the magnitude of a uniform magnetic field is usually a given, the magnitude of the field surrounding a wire can be determined by using an equation. Determining direction of the force on the charge will require you to use both versions of the right-hand rule. First, you must determine the direction of the magnetic field of the wire. Use the curled finger version to find the direction of the magnetic field on the side of the wire where the charge is moving. Next, you must determine the force on the moving charge using the straight finger version and seeing which way the palm is pushing.

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