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Magnetism is a fundamental force of nature that causes certain materials to attract or repel others. You experience magnetism daily-whether in the fridge magnets holding notes, credit card strips, or the compass guiding travelers. At its heart, magnetism arises from tiny charged particles in motion inside atoms.
Magnets have two ends called magnetic poles. These are labelled as north (N) and south (S). Like poles repel, and unlike poles attract. Natural magnets, such as lodestone, occur in nature, whereas artificial magnets-like bar magnets-are made by humans for various uses.
Understanding magnetism is key to grasping many electrical devices and natural phenomena, linking closely with electricity and forces acting on moving charges. Let's start with the basics of magnetic fields.
A magnetic field is a region around a magnet where magnetic forces can be felt. We cannot see magnetic fields directly, but we represent them using magnetic field lines.
Magnetic field lines:
This idea helps visualize the invisible magnetic influence in space surrounding magnets.
Figure: Magnetic field lines emerging from the north pole and entering the south pole of a bar magnet.
In 1820, Hans Christian Oersted discovered a key connection: an electric current produces a magnetic field. When a current flows through a wire, a magnetic field forms around the wire in circular loops.
This means that electricity and magnetism are deeply linked-forming the basis of electromagnetism. The direction of these magnetic circles around a straight conductor can be predicted by the Right-Hand Thumb Rule: if you hold the conductor with your right hand, thumb pointing in the current's direction, your curled fingers show the magnetic field's circular direction.
Figure: Concentric magnetic field circles around a vertical current-carrying wire. Current flows upward (red arrow), field lines circle counterclockwise (blue arrows).
A magnetic field not only is produced by currents but also acts on currents. A force acts on a wire carrying current when placed in a magnetic field, explained by Fleming's Left-Hand Rule:
The magnetic force's magnitude on a wire length \(L\) carrying current \(I\) in a magnetic field \(B\), at angle \(\theta\) to the wire, is given by:
Magnetic Force Formula:
\( F = I L B \sin\theta \)
where
A 0.5 m long wire carrying 3 A current is placed perpendicular to a magnetic field of 0.2 T. Find the force on the wire.
Solution:
Force on the wire is 0.3 newtons.
When the magnetic field through a coil or loop changes, it creates an electrical effect - an induced emf (electromotive force) or voltage. This phenomenon is electromagnetic induction. Michael Faraday discovered this in 1831 and formulated what is now known as Faraday's Law of Induction.
Faraday's Law states that the induced emf in a coil is proportional to the rate of change of magnetic flux through it:
\( E = - \frac{d\Phi}{dt} \)
where
The negative sign is explained by Lenz's Law, which says the induced current opposes the change causing it. In other words, the induced emf creates a current whose magnetic field tries to keep the original magnetic flux constant.
graph TD A[Change in Magnetic Flux] --> B[Induced emf \(E\)] B --> C[Induced Current] C --> D[Magnetic Field Opposes Change] D --> A
This opposing action is nature's way of conserving energy and preventing runaway feedback.
Step 1: Identify known quantities:
\(L = 0.5\, \text{m},\, I = 3\, \text{A},\, B = 0.2\, \text{T},\, \theta = 90^\circ\)
Step 2: Since the wire is perpendicular to the magnetic field, \(\sin 90^\circ = 1\).
Step 3: Apply the formula \(F = I L B \sin\theta\):
\(F = 3 \times 0.5 \times 0.2 \times 1 = 0.3\, \text{N}\)
Answer: The magnetic force acting on the wire is 0.3 newtons.
Step 1: Given length \(L = 1.0\, \text{m}\), velocity \(v = 5\, \text{m/s}\), magnetic field \(B = 0.3\, \text{T}\).
Step 2: Since conductor moves perpendicular to magnetic field, use formula \(E = B L v\).
Step 3: Calculate emf:
\(E = 0.3 \times 1.0 \times 5 = 1.5\, \text{V}\)
Answer: The induced emf is 1.5 volts.
Step 1: Given current \(I=10\, \text{A}\), distance \(r=0.1\, \text{m}\), permeability of free space \(\mu_0 = 4\pi \times 10^{-7} \, \text{T·m/A}\).
Step 2: Use formula for magnetic field around wire:
\[ B = \frac{\mu_0 I}{2 \pi r} \]
Step 3: Substitute values:
\[ B = \frac{4\pi \times 10^{-7} \times 10}{2 \pi \times 0.1} = \frac{4\pi \times 10^{-6}}{0.2 \pi} = \frac{4 \times 10^{-6}}{0.2} = 2 \times 10^{-5} \, \text{T} \]
Answer: The magnetic field 0.1 m from the wire is \(2 \times 10^{-5}\) tesla.
Step 1: Given current \(I=4\, \text{A}\), area \(A=0.02\, \text{m}^2\), magnetic field \(B=0.5\, \text{T}\), angle \(\theta=60^\circ\) (between field and normal to loop plane).
Step 2: Use torque formula on current loop:
\[ \tau = I A B \sin\theta \]
Step 3: Calculate sin 60° = \(\sqrt{3}/2 \approx 0.866\).
Step 4: Substitute values:
\[ \tau = 4 \times 0.02 \times 0.5 \times 0.866 = 0.03464\, \text{N·m} \]
Answer: The torque on the current loop is approximately 0.0346 newton-meters.
Step 1: Current direction is north (point middle finger north).
Step 2: Magnetic field direction is vertically down (point forefinger down).
Step 3: Using Fleming's Left-Hand Rule, thumb points to force direction.
Step 4: Thumb direction is towards west.
Answer: Force on the conductor is directed towards the west.
When to use: When determining magnetic force direction or induced current direction.
When to use: Always before starting numerical problems.
When to use: When angle is unknown or estimate maximum force.
When to use: During formula revision and application.
When to use: Problems involving multiple concepts such as moving conductors in fields.
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