Forces on Current Carrying Wires in Magnetic Fields Chapter 19 Herriman High School - AP Physics 2

Section 19.1: Magnets A magnet consists of two poles. If we consider a bar magnet one end is called the north pole and the other the south pole. In a compass the north pole of the magnet points toward the geographic north pole of the earth and the south pole of the magnet points toward the geographic south pole of the earth. Like electric charges – magnetic material follow the property that opposites attract and likes repel. The Geographic North pole of the earth is actually its magnetic south pole. Herriman High School - AP Physics 2

Section 19.3: Magnetic Fields Just like an electric charge develops a field around it – a magnet also creates a field effect around itself. Conventionally Magnetic Field lines point outward from the north pole and terminate inward at the south pole. A stationary charged particle is not affected by a stationary magnetic field, however a charged particle moving through a magnetic field experiences a force. The magnitude of this force is defined as: q = charge of particle v = velocity of the particle in m/s B is the magnetic field strength in tesla (T) θ = the angle between the magnetic field and the motion of the particle. Herriman High School - AP Physics 2

The Direction of the Magnetic Force on a Charged Particle. B = magnetic field strength is measured in Tesla or weber per square meter, 1 T = 1Wb/m 2, often however it is more convenient to use the gauss (G) where 1 T = 10 4 G. From the Force equation, you can also see that the force exerted is at its maximum when the particle is moving perpendicular to the magnetic field and drops to zero when the particle moves parallel to the magnetic field. Determination of the direction of the force is done by using the right hand rule. Point the fingers of the right hand in the direction the particle is moving. Point your palm in the direction of the magnetic field. Your thumb will now point in the direction of the force. Herriman High School - AP Physics 2

Sample Problem: A proton moves with a speed of 1 x 10 5 m/s in the earth’s magnetic field which has a value of 55 μT at a particular location. When the proton moves eastward, the magnetic force is directed upward, and when it moves northward, no magnetic force acts on it. a) What is the direction of the magnetic field? b) What is the strength of the magnetic field when the proton moves eastward? Herriman High School - AP Physics 2

Solution Use the right hand rule to get the direction of the magnetic field – north or south. (North) Substitute to get the magnitude of the field: Herriman High School - AP Physics 2

Section 19.4: Magnetic Force on a Current Carrying Conductor Force on a current carrying wire If a moving charged particle experiences a force because of a magnetic field then it makes sense that a current carrying conductor would too. (Remember that current is the movement of charge in a certain amount of time.) Herriman High School - AP Physics 2

Magnetic force on a wire The force on a wire follows the same right hand rule. B = Magnetic Field I = current in amperes L = length of the wire θ = angle between the field and the wire. Herriman High School - AP Physics 2

Sample Problem: A wire carries a current of 22 A directed west to east. The magnetic field at this location is directed south to north with a strength of 0.5 x T. Find the magnitude and direction of the magnetic force on a 36 meter length of wire. Magnitude: F = BIL sin θ F = (5 x T)(22 A)(36 m)sin 90 ° =.0396 N Direction Fingers point east, palm north, so thumb is upward. Force is upward. Herriman High School - AP Physics 2

Section 19.5: Torque on a current carrying loop If the wire is bent in the form of a loop how will the forces act? The two opposing forces will produce a torque Note that the Force will be the greatest when B is parallel to the plane of the loop! Why? Because when it is parallel to the rectangular loop part of the loop will be parallel to the magnetic field but the other part will be exactly perpendicular Herriman High School - AP Physics 2

The Formula τ =torque N is the number of turns or loops in the wire B is the Mag field A is the area of the loop θ is the angle between the Magnetic field and the line perpendicular to the loop μ is called the magnetic moment of the loop. So torque can also equal Herriman High School - AP Physics 2

Sample Problem A circular wire of radius 1 m is placed in a magnetic field of 0.5 T. The normal of the plane of the loop makes an angle of 30 degrees with the magnetic field and the current is 2 A moving counter clockwise around the loop. Find the magnetic moment of the loop and the magnitude of the torque at this instant. Herriman High School - AP Physics 2

Solution: μ = IAN = (2 A)(3.14 m 2 )(1) = 6.28 A*m 2 T = μBsinθ = ( 6.28 A*m 2 )(0.5 T)(sin 30) = 1.57 N*m. Herriman High School - AP Physics 2

Section 19.7: Magnetic Field of a Long Straight Wire and Ampere’s Law Current carrying wires actually produce their own magnetic field. The magnetic field surrounds the wire. Herriman High School - AP Physics 2

Right hand rule for wires Your thumb heads in the direction of the current (I) Your fingers wrap around the wire in the direction of the magnetic field Herriman High School - AP Physics 2

The Formula B stands for the magnetic field strength r is the distance from the wire μ 0 =4 π x10 -7 Tm/A AKA the permeability of free space. Herriman High School - AP Physics 2

Finding the Magnetic field for more than one wire If there are two wires you need to find the magnetic field for each wire Find the direction of the magnetic field for each wire If the magnetic fields are in the same direction you may add If they are in opposite directions subtract Herriman High School - AP Physics 2

Sample Problem Problem: A long straight wire carries a current of 5 A. Calculate the magnetic field of the wire 4 mm away. Solution: Herriman High School - AP Physics 2

Section 19.8: Magnetic Force Between Two Parallel Conductors µ 0 – permeability of free space d – the distance separating the 2 wires. The forces are attractive if the currents are in the same direction Repulsive if in opposite directions. Herriman High School - AP Physics 2

Sample Problem Two wires, each having a weight per unit length of 1 x N/m, are parallel with one directly above the other. Assume the wires carry currents that are equal in magnitude and opposite in direction. The wires are 0.1 meters apart and the sum of the magnetic and gravitational force on the upper wire is zero. Find the current in the wires, neglect Earth’s magnetic field. F grav + F mag = 0 Herriman High School - AP Physics 2