NUSH PC3131 Electromagnetism

Electromagnetism Ethan Chew M24304 Contents of this notes package: Chapter 11 PC3131, Electromagnetism Chapter 12 PC3131, Electromagnetic Induction Bridging the Gap Electricity and magnetism are not two separate phenomena. Let’s explore how these two fundamental properties of nature interact with each other! Recall your abbreviations: I - current, B - magnetic field. Before we can visualise their interactions, we must first establish a way to express vectors in 3D space on our 2D paper. The following shows the notations of current / magnetic field vectors pointing in the third dimension: Now, consider the case where a current is flowing through a straight wire out of the page, like so:

The core concept of Electromagnetism is that a moving charge generates a magnetic field. The grey lines surrounding the current (going out of the page) is the magnetic field generated by said current. The magnetic field strength gets weaker the further we move from the wire (indicated by the increasing space between the concentric circles). Now, you may realise I’ve indicated with an arrow the direction of the magnetic field. This is just a consequence of whether the current is flowing out of the page or into the page. The direction can be determined by the Right-Hand Grip Rule: 1. Stick your thumb out and curl your fingers towards your palm. 2. Your thumb corresponds to the current direction, and the curling of your fingers represents the direction of the magnetic field.

When compasses are placed around the vertical wire, their needles point tangentially to the magnetic field, with North pointing in the same direction as the indicated arrow. Can you infer what the direction of the magnetic field is for a current going into the page? Solenoids and Electromagnets If a straight wire can generate a magnetic field, then a coil of wire ( solenoid ) can definitely also generate a magnetic field! However, the nature of this field is different. Remember that direction of current is taken conventionally , i.e. the flow of positive charges from the positive terminal, through the entire circuit, and ending at the negative terminal. Here, we may use the Right-Hand Grip Rule slightly differently: 1. Curl your fingers in the direction of the current looping in the coil. 2. Your thumb points in the direction in which the magnetic field leaves the loop, i.e. the North pole . The solenoid has a uniform magnetic field within it, and a magnetic field pattern similar to that of a bar magnet outside of it. A soft magnetic material (iron) may be inserted within the solenoid to increase the strength of the magnetic field, as the magnetic domains of the material align. This brings us to electromagnets.

When solenoids and soft magnetic materials come together, we get electromagnets. In Electromagnetism, there are many different applications of electromagnets. When answering application questions, take note of three things: - The nature of how the electromagnet is magnetised - which direction is the current flowing? - The status of the circuit - closed or open? - The effect of the electromagnet - what does it control? Electrical Energy to Kinetic Energy When a current-carrying conductor interacts with an external magnetic field, a magnetic force is produced that acts on the conductor. To find the direction of the magnetic force acting on this conductor, we apply Fleming’s Left-Hand Rule: 1. Position your thumb and index finger at 90 degrees to each other, as if you are mimicking holding a gun. 2. Extend your middle finger out such that it is 90 degrees from your index finger.

3. Your thumb represents the magnetic force , your index finger represents the direction of the magnetic field (N to S) and your middle finger represents the direction of conventional current (positive to negative). In the above example, the current points up and the magnetic field is leftwards. Hence, the magnetic force must be out of the page . It helps to remember this as FBI - Force (F), Magnetic field (B), Current (I). What happens when the magnetic field points rightwards? What happens when the current points into the page? What directions would the current and magnetic field point if the magnetic force was downwards? NOTE: There is only a force if B and I are not parallel / antiparallel. If they are, F = 0. Single Charge in Magnetic Field We can also apply Fleming’s Left Hand rule to single charges in a magnetic field. If the velocity of the charge and magnetic field direction are perpendicular to each other, we can trace the path of the charge. As the magnetic force will also be perpendicular to the velocity of the charge, this results in the charge experiencing uniform circular motion (assuming the magnetic field can contain the entire motion).

If there is not just one charge but a beam of charges of the same sign, we will observe the beam deflecting according to the circular path. Observe the diagram above. The positive charge moves to the right, and the magnetic field goes into the page, resulting in a magnetic force upwards. If we replace this with a negative charge, what would happen to the direction of the magnetic force? Interaction of Two Current-Carrying Conductors Consider the scenario where two conductors are carrying current in the same direction. Each current can be affected by one or more surrounding magnetic fields, therefore resulting in a magnetic force acting on the conductor.

Note that because the magnetic field generated by each wire is circular , we take the tangent of the circle to be the direction of our magnetic field. In the above diagram, the direction of the magnetic field from wire 2 on wire 1 is downwards (red arrow). Focusing on wire 1, we can now apply Fleming’s Left Hand Rule to discover that the magnetic force on wire 1 is to the right . If we do the same with wire 2, we will find that wire 2 experiences a magnetic force to the left . Thus we can conclude that the two conductors will attract each other. What if the conductors are carrying charges in opposite directions? Torque on a Coil A coil of wire within a uniform magnetic field may experience a net force or net torque due to the multiple directions in which the wires in the coil are oriented. For each segment of the coil, we can use Fleming’s Left-Hand Rule to determine the magnetic force acting on it. To check your answer, you may opt to vectorise the loop current . What does this mean? Using the Right-Hand Grip