Magnetic Fields
Comparing electric and magnetic fields
Similarly to electric field lines, magnetic field lines display the magnitude and direction of a magnetic field. This is indicated by the picture below where the field lines travel from the north to south pole. A difference between a magnetic field and an electric field is that an electric field can be created by one single charge, however a magnetic field cannot be created by one pole alone. There must be a north and a south to form a magnetic field.
Similarly to electric field lines, magnetic field lines display the magnitude and direction of a magnetic field. This is indicated by the picture below where the field lines travel from the north to south pole. A difference between a magnetic field and an electric field is that an electric field can be created by one single charge, however a magnetic field cannot be created by one pole alone. There must be a north and a south to form a magnetic field.
Permanent Magnets/ Bar Magnets
Using iron fillings and a bar magnet, an image can help explain some concepts of magnetic fields. The magnetic field of the bar magnet is not visible, but the iron fillings follow the path of the magnetic field. This shows the direction of these lines and where they are concentrated. It can be concluded that the magnetic field is denser at the poles. Another conclusion that can be taken from bar magnets, is that the north and south poles attract while the like poles repel.
The Earth
The Earth is one large bar magnet. Due to its iron core, it has a magnetic north and a magnetic south pole. However, Earth’s magnetic poles are different from its geological poles. Earth’s north pole is actually its magnetic south pole. Earth’s magnetic field provides important applications in nature such as animal migration.
Current In Wire
Running current through a wire will create a magnetic field that circles around the wire. If you curl your right hand, your fingers will be in the direction of the magnetic field and your thumb will point in the direction of the current. Using your right hand will provide results for conventional current, and using your left hand will provide results for electron flow. This is known as the right hand rule for a straight conductor.
Loop Of Wire
Twisting the wire into a loop intensifies the magnetic field at the centre of the loop. This is because the magnetic field lines in the middle of the loop are closer together. The right hand rule for a straight conductor can still be used.
Solenoid
If one loop can make the magnetic field stronger, than continuous loops will increase the field strength further. This coil is called a solenoid. The field strength in the middle of the coil is where it is the strongest since the field lines are closest together. The right hand rule for a solenoid can be used. If you curl your hand and have your thumb pointing out, then your fingers will point in the direction of the current and your thumb will point in the north direction of the magnetic field.
Using iron fillings and a bar magnet, an image can help explain some concepts of magnetic fields. The magnetic field of the bar magnet is not visible, but the iron fillings follow the path of the magnetic field. This shows the direction of these lines and where they are concentrated. It can be concluded that the magnetic field is denser at the poles. Another conclusion that can be taken from bar magnets, is that the north and south poles attract while the like poles repel.
The Earth
The Earth is one large bar magnet. Due to its iron core, it has a magnetic north and a magnetic south pole. However, Earth’s magnetic poles are different from its geological poles. Earth’s north pole is actually its magnetic south pole. Earth’s magnetic field provides important applications in nature such as animal migration.
Current In Wire
Running current through a wire will create a magnetic field that circles around the wire. If you curl your right hand, your fingers will be in the direction of the magnetic field and your thumb will point in the direction of the current. Using your right hand will provide results for conventional current, and using your left hand will provide results for electron flow. This is known as the right hand rule for a straight conductor.
Loop Of Wire
Twisting the wire into a loop intensifies the magnetic field at the centre of the loop. This is because the magnetic field lines in the middle of the loop are closer together. The right hand rule for a straight conductor can still be used.
Solenoid
If one loop can make the magnetic field stronger, than continuous loops will increase the field strength further. This coil is called a solenoid. The field strength in the middle of the coil is where it is the strongest since the field lines are closest together. The right hand rule for a solenoid can be used. If you curl your hand and have your thumb pointing out, then your fingers will point in the direction of the current and your thumb will point in the north direction of the magnetic field.
A magnetic force is felt by a charge if it enters a magnetic field. These two equations can quantify this force.
Magnetic Force Equations
-The magnetic force is the charge (q) multiplied by the velocity (v) multiplied by the external magnetic field (B). The charge, velocity, and field are proportional to the force.
-The magnetic force is also the current (I) multiplied but the length of the wire (L) multiplied by the external field (B). The current, length, and field, are proportional to the force.
These equations are important in an MRI as this machine uses magnetic fields that creates a magnetic force. It is essential to find the body's limitations to the external field so the machine does not exceed beyond it.
Magnetic Force Equations
-The magnetic force is the charge (q) multiplied by the velocity (v) multiplied by the external magnetic field (B). The charge, velocity, and field are proportional to the force.
-The magnetic force is also the current (I) multiplied but the length of the wire (L) multiplied by the external field (B). The current, length, and field, are proportional to the force.
These equations are important in an MRI as this machine uses magnetic fields that creates a magnetic force. It is essential to find the body's limitations to the external field so the machine does not exceed beyond it.
Felix Bloch created an important and useful equation explaining the origin and properties of magnetic resonance signals. The numerous nuclei in our bodies can be represented by a vector M, magnetization. Comparatively to the proton's angular spin, the vector M would be the same. Therefore M has three components, Mx(t), My(t), and Mz(t), where t is time. Mx(t and My(t) are transverse components while Mz(t) is a longitudinal component.
τ = M x B where torque (τ) is the cross product of the magnetization (M) and external field (B). An external force on M produces it to twist.
Two relaxation constants are T1 and T2, which account for the reestablishment of the thermal equilibrium of the nuclear magnetization after generation of the MRI signal. T1 showed the increase in the longitudinal magnetization (Mz) while T2 showed the decrease in the transverse components (Mx and My). He then created these three equations which predict M's spiralling precession.
Mx(t) = Mo e −t/T2 sin ωt
My(t) = Mo e−t/T2 cos ωt
Mz(t) = Mo (1 − e−t/T1)
τ = M x B where torque (τ) is the cross product of the magnetization (M) and external field (B). An external force on M produces it to twist.
Two relaxation constants are T1 and T2, which account for the reestablishment of the thermal equilibrium of the nuclear magnetization after generation of the MRI signal. T1 showed the increase in the longitudinal magnetization (Mz) while T2 showed the decrease in the transverse components (Mx and My). He then created these three equations which predict M's spiralling precession.
Mx(t) = Mo e −t/T2 sin ωt
My(t) = Mo e−t/T2 cos ωt
Mz(t) = Mo (1 − e−t/T1)