 # Discuss the effect on the magnitude of the force on a current-carrying con- ductor of variations in the strength of the magnetic field in which it is located, the magnitude of the current in the conductor, the length of the conductor in the ex- ternal magnetic field and the angle between the direction of the external magnetic field and the direction of the length of the conductor

All of these variables can be summarised by the formula F = BIlsinθ. When the strength of the field increases, so does force. When magnitude of the current is increased, and when the length of the conductor is increased, force increases. As far as angle goes, force is at a maximum when the angle is 90 degrees with the conductor perpendicular to the field, and force is zero when the conductor is parallel to the magnetic field.

# Describe qualitatively and quantitatively the force between long parallel current carrying conductors

You may want to model this yourself by using the right-hand grip rule to determine how the magnetic fields in each wire interact to cause them to attract. Essentially, the wire on the right side has a magnetic field running upwards through the other wire. Then use the right hand palm rule to work out the direction of force.

The force between parallel current carrying conductors depends on the direction of current flow. If current flow is in the same direction, then the wires will attract. If it is in opposite directions, then the wires will repel. The formula is $\frac {F}{l} = \frac {kI_1 I_2}{d}$ and shows that as length and currents increase, force increases, and that as distance increases, force decreases in a linear relationship. This follows from the formula $B = \frac {kI}{d}$ which calculates the strength of the magnetic field produced by a conducting wire with current I, at distance d from the wire. Remember- Wires with current flowing in the same direction attract each other.

# Describe the forces experienced by a current-carrying loop in a magnetic field and describe the net result of the forces

A current carrying loop will experience force due to the motor effect. Perpendicular sides of the loop have current moving in opposite directions, so they experience opposite forces. If the coil is able to pivot around its centre, one of the sides will experience an upward force, and the other will experience a downwards force. Because of the structure of the loop, each of the sides produces torque, as they experience a force acting tangentially to the pivot point when the loop is horizontal. This causes the loop to rotate. Remember- Opposite sides of the loop with have current flowing in opposite directions, so they experience opposite force, so the coil rotates.

# Perform a first-hand investigation to demonstrate the motor effect

In our experiment, we had a wire sitting on a piece of wood. Magnets on either side of the wood set up a magnetic field passing through the wire, with the field lines perpendicular to the wire (in the horizontal plane). When we passed a current through the wire in the correct direction (according to the right-hand palm rule) the wire jumped upwards, due to the motor effect where moving charge in a magnetic field experiences force. The setup could only be used intermittently, because there was no load in the circuit. This meant large currents flowed through the wire, and operation for more than a few seconds caused dangerous overheating and the power supply to shut down.

Remember- The experiment made a wire jump up due to the motor effect.

# Define torque as the turning moment of a force using T = Fd

Broadly speaking, there are 2 forms of motion. The first is linear motion, which occurs when an object travels through space. Examples of this include the motion of a ball as it is thrown, or the motion of the Earth around the sun. In both cases, the spatial position of the object changes. The second form of motion is rotational motion, which occurs when an object spins. Examples of this include the spinning of a CD in a drive, or the rotation of a fan. In both these cases, the objects are not moving through space but instead remain stationary while they rotate (the spinning of car wheels is also an example of rotational motion, but in that case the wheels also have a component of linear motion as they are moving through space with the car). Linear motion occurs when a linear force is applied to an object, for example when something is pushed or pulled. Rotational motion occurs when a rotational force is applied to an object, such as when it is twisted. The difference between the two is subtle. Linear force is a vector with both magnitude and direction. When a linear force is applied directly in line with an object’s centre of gravity, then the object will travel through space without rotating. However, if a linear force is applied off centre, some distance away from the object’s centre of gravity, then in addition to moving through space the object will also rotate around its centre of gravity. The rotational force that has been applied to cause the object to rotate is equal to Fd, where F is the magnitude of the linear force, and d is the distance between the point at which the force is applied and the object’s centre of gravity. For simplicity, linear force is referred to simply as force, while rotational force is referred to as torque.

Torque can be considered the turning force on an object. It occurs when a force is applied to an object tangentially rather than straight at it. The torque depends on the force and the perpendicular distance from the pivot point, which is equal to Fd. # Identify that the motor effect is due to the force acting on a current-carrying conductor in a magnetic field

The motor effect is caused by the moving of electrons in a magnetic field. When placed in a magnetic field, moving charge experiences a force. This force is dependant on the direction of the field. When charge is moved through a wire, the wire experiences a force. This force is what constitutes the motor effect- the conversion of moving electric charge in a magnetic field into kinetic energy.

Remember- Moving charge in a magnetic field experiences force, and this can be used to move a conductor with electrons moving through it.

# Identify data sources, gather and process information to qualitatively describe the application of the motor effect in the galvanometer and the loudspeaker

Make sure you can comprehensively and clearly describe how the galvanometer and loudspeaker work, and ensure that you explain how the motor effect is used in these applications.

The galvanometer and the loudspeaker are two devices which rely on the motor effect for their operation. The motor effect is where moving charge in a magnetic field experiences force, and leads to wires carrying current in a magnetic field experiencing force. In a loudspeaker, a solenoid is immersed in a static magnetic field. The solenoid is free to move as it is alternately attracted and repelled by the permanent magnet. This movement occurs because when current is passed through the solenoid, it causes the solenoid to experience force. This force moves the solenoid in motion that corresponds to the current being fed into it. If the current being fed in corresponds to an audio wave, the solenoid will oscillate in the same way as the audio wave. Because the solenoid is connected to a large cone, the solenoid causes the cone to vibrate as it moves. These vibrations result in the formation of pressure waves in the air, which are heard as sound. So the operation of a loudspeaker depends on the motor effect to move the solenoid, converting electrical energy into sound energy. In a galvanometer, a coil of wire is wrapped around an iron core onto which is attached a needle. This entire assembly is free to rotate. A stator consisting of permanent magnets produces a radial magnetic field immersing the solenoid. The iron core is used to direct and intensify the magnetic field. When current is passed through the solenoid, a force results from the motor effect. Torque is thus produced, the same as in a motor, and causes the solenoid and the needle to rotate. Because a radial magnetic field is used, the torque produced is constant regardless of how far the coil is deflected. However, the galvanometer also incorporates a spring that is attached to the solenoid. The solenoid compresses the spring as it rotates, and in this way the solenoid rotates up until the torque experienced by the solenoid is fully countered by the spring. Because a radial magnetic field is used, the coil experiences constant torque. Further, the force exerted by the spring also increases linearly (using the formula F = −kx which is outside the scope of the syllabus, where k is a constant describing the properties of the spring, and x is the degree to which it is compressed). Because torque and spring force scale linearly with current, a linear scale can be developed linking current to coil rotation. As the coil is connected to a needle, this setup can be used to assess how much current is flowing through a circuit.

Remember- A loudspeaker uses the motor effect to move the cone, and a galvanometer uses the motor effect and a radial magnetic field to measure current through the strength of the motor effect.

# Describe the main features of a DC electric motor and the role of each feature

Direct Current (DC) motors consist essentially of 3 parts- the stator, the armature, and the com- mutator. In order for the motor effect to occur, a magnetic field is required. The stator consists of permanent magnets or coils of wire that produce a magnetic field that runs through the centre of the motor. The stator does not move during the operation of the motor, and is arranged around the armature which is at the centre of the motor. The stator provides a magnetic field that immerses the armature. The armature consists of loops of wire wrapped around a ferromagnetic core that experience a force when current is passed through them in the presence of a magnetic field. The armature is free to rotate, and is connected to whatever the motor is driving. The commutator is attached to one end of the armature, and is the means by which electricity is passed into the armature. It consists of a ring shaped conductor that is split into two parts, each part connected to one end of the coil that makes up the armature. Brushes on either side are connected to the circuit, one positive, one negative. Current flows through one of the brushes, into the commutator, then through the armature, back to the commutator, and out into the rest of the circuit via the other brush. The role of the commutator is to reverse the direction of current in the armature every half-turn. This causes the force experienced by the armature to reverse, and ensures that the torque experienced by the armature always occurs in the same direction.

Remember- Stator, armature, commutator, brushes.

# Identify that the required magnetic fields in DC motors can be produced by current-carrying coils or permanent magnets

In order for a DC motor to operate, the armature must be immersed in a magnetic field. This allows moving charge in the armature to generate force. How this magnetic field is generated however, is immaterial. Permanent magnets as well as current-carrying coils can provide this field. Moving charge produces a magnetic field, and so current carrying coils can produce magnetic fields similar to those produced by bar magnets. This principle can be used to generate the field in a DC motor, just like with permanent magnets. If electromagnets are used, the wire is usually wrapped around an iron core to increase the strength of the field.

Remember- A DC motor needs a magnetic field, and this can be provided through either current- carrying field coils or through a permanent magnet.