Quick questions on Magnetic flux and flux density: HSC Physics Module 6

The magnetic flux density (often just called the magnetic field) $\vec{B}$ at a point is a vector describing the strength and direction of the magnetic field there. It is what a compass needle aligns with, and it determines the force on a moving charge ($F = qvB$) or on a current ($F = BIL \sin \theta$).

<!-- Diagram: flux through a coil at angle theta | reviewed 2026-05-21 --> <svg class="fig" viewBox="0 0 460 280" role="img" aria-labelledby="flux-t flux-d"> <title id="flux-t">Magnetic flux through a tilted coil</title> <desc id="flux-d">A flat rectangular coil of area A is tilted so that its normal vector n makes an angle theta with the uniform magnetic field B. Field lines pass through the coil; the flux equals B A cosine theta. When the normal is aligned with B (theta zero), flux is a maximum. When the normal is perpendicular to B (theta ninety), flux is zero.</desc> <defs> <marker id="fl-arr" viewBox="0 0 10 10" refX="9" refY="5" markerWidth="6" markerHeight="6" orient="auto"> <path d="M0 0 L10 5 L0 10 z" fill="var(--accent)"/> </marker> </defs> <g stroke="var(--accent)" stroke-width="1.4" fill="none"> <line x1="40" y1="70" x2="420" y2="70" marker-end="url(#fl-arr)"/> <line x1="40" y1="110" x2="420" y2="110" marker-end="url(#fl-arr)"/> <line x1="40" y1="150" x2="420" y2="150" marker-end="url(#fl-arr)"/> <line x1="40" y1="190" x2="420" y2="190" marker-end="url(#fl-arr)"/> </g> <text x="404" y="62" font-size="13" font-weight="700" class="var accent">B</text> <g transform="translate(220 130) rotate(-30)"> <rect x="-60" y="-50" width="120" height="100" fill="var(--paper)" stroke="var(--ink)" stroke-width="1.6"/> <line x1="0" y1="0" x2="80" y2="0" stroke="var(--ink)" stroke-width="1.8" marker-end="url(#fl-arr)"/> <text x="68" y="-8" font-size="13" font-weight="700" class="var">n</text> </g> <path d="M 290 130 A 50 50 0 0 0 290 70" fill="none" stroke="var(--ink)" stroke-width="1"/> <text x="304" y="100" font-size="12" class="var">θ</text> <text x="230" y="260" text-anchor="middle" font-size="11" class="muted">Φ = B A cos θ; θ is the angle between B and the area normal n.</text> </svg>

The $\theta$ in $\Phi = B A \cos \theta$ is the angle between $\vec{B}$ and the normal to the surface, not between $\vec{B}$ and the surface itself. Questions sometimes give the angle between the field and the plane of a coil; you must take the complement.

A coil of $N$ turns links flux $N$ times (each turn intercepts the same flux, in series). The flux linkage is:

Define magnetic flux density and magnetic flux, giving SI units of each. [2 marks]

A circular coil of radius $5.0 \text{ cm}$ sits with its plane at $30^{\circ}$ to a uniform field of $0.40 \text{ T}$. Calculate the flux linking the coil. [3 marks]

A rectangular loop $0.20 \text{ m} \times 0.10 \text{ m}$ is placed in a field $B = 0.50 \text{ T}$. (a) Calculate the maximum flux through the loop. (b) Find the flux when the loop normal is at $45^{\circ}$ to $\vec{B}$.