PMDC Unit 46 · 4 outcomes

Electromagnetism

Unit 10 is the magnetic field as a flux density, flux as B · A, and what a charged particle does when it flies across B — a circle, with F always sideways.

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10.1

Magnetic flux density

PMDC: Define magnetic flux density and its units.

Magnetic flux density B (the magnetic field) tells you how strong and which way the field is. The force on a charge moving across the field is $F = q$ v B sin $θ$ . If that force is $1 N$ on a $1 C$ charge moving at $1 m$ s⁻¹ perpendicular to B, then B is 1 tesla.

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B = F / (I L) = 6/ (2 \times 1.5) = 2 T

B from $F = q$ v B sin $θ$
$1 T = 1 N A^{- 1} m^{- 1} = 1 Wb m^{- 2}$

Hold these

B is a vector. Direction is the field-line direction (N → S outside a magnet).
The tesla is large. The Earth’s field is about $5 \times 1 0^{- 5}$ T.

10.2

Magnetic flux

PMDC: Describe magnetic flux Φ as the scalar product of B and area A: Φ_B = B_⊥ A = B · A.

Flux is how many field lines punch through a loop. Face the loop straight at B and flux is BA. Tilt the loop and only the perpendicular part of B counts. If B is in the plane of the loop, flux is zero.

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Φ = B A cos θ = 6 Wb

$Φ = B A cos θ = B \cdot A$
$θ$ : angle between B and the normal to A
unit: weber (Wb) $1 Wb = 1 T$ m²

Hold these

Flux is a scalar (a signed one).
Turn the loop $9 0^{\circ}$ and $Φ$ goes to zero even if B is still there.

10.3

Path of a charge perpendicular to B

PMDC: Describe quantitatively the path followed by a charged particle shot into a magnetic field perpendicular to the field.

$F = q$ v B is perpendicular to v, so it cannot speed the particle up or slow it down. It only bends the path. Perpendicular injection into a uniform B: a circle. The magnetic force is the centripetal force.

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v ⊥

B \Rightarrow c i r c u l a r

path

$q v B = m v^{2} / r$
$r = m v / (q B)$
$T = 2 π$ m / (q B) (period, independent of v)

Hold these

Faster particle: larger circle, same time around.
Stronger B: tighter circle.

10.4

Force on a charge in uniform B

PMDC: Explain that a force may act on a charged particle in a uniform magnetic field.

The force needs three things: charge, motion, and a component of v across B. Resting charges feel no magnetic force. Motion parallel to B: $θ$ = 0, $F = 0$ , the particle coasts in a straight line. At an angle, the parallel part of v is untouched and the perpendicular part circles — a helix.

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F = q v B sin θ = 24 N

$F = q v B sin θ$
$F = 0$ if $v = 0$ or v ∥ B
direction: right-hand rule for +q (flip for −q)

Hold these

Magnetic force does no work (always ⊥ v), so KE stays the same.
Uniform B can circle a charge. It cannot speed it up.

Unit 46 formula sheet

Write these until they are cheaper than thinking, then open the quiz.

B from $F = q$ v B sin $θ$
$1 T = 1 N A^{- 1} m^{- 1} = 1 Wb m^{- 2}$
$Φ = B A cos θ = B \cdot A$
$θ$ : angle between B and the normal to A
unit: weber (Wb) $1 Wb = 1 T$ m²
$q v B = m v^{2} / r$
$r = m v / (q B)$
$T = 2 π$ m / (q B) (period, independent of v)
$F = q v B sin θ$
$F = 0$ if $v = 0$ or v ∥ B
direction: right-hand rule for +q (flip for −q)

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