2023 A/L Physics Past Paper · Question 25 (English Medium)

Answer: (2) only (A) and (B) are true.

What the question asks

We want: which of the statements (A), (B) and (C) about the magnetic force on a current carrying wire are true.

What each letter means:

$F$ ($\text{N}$): the magnetic force on the wire.

$B$ ($\text{T}$): the magnetic flux density of the field.

$I$ ($\text{A}$): the current in the wire.

$l$ ($\text{m}$): the length of the wire.

$\theta$ ($^\circ$): the angle between the wire and the field.

Relevant theory

If the moving charge is considered to be equivalent to a current $I$ flowing along a conductor of length $l$ placed along the direction of the motion of the charge, then the force acting on it,

$F = BIl \sin\theta$

That is when the conductor is parallel to the magnetic field, no force acts on it even if a current passes through the conductor.

Reading the options

The options are combinations of (A), (B) and (C).

We test each statement on its own.

The first quote gives the force on a length $l$ of wire. The second quote says that a wire along the field feels no force. So the direction of each bit of wire matters.

For example, think of a long ribbon held in a steady wind. A longer ribbon catches more wind, so it is pushed more.

Bend the ribbon into a zigzag. Each bit is pushed sideways, but now the bits point different ways, so the pushes do not add up in one direction. The total push is not the same as for the straight ribbon.

A magnetic force on a wire behaves in the same way, bit by bit.

Reasoning and calculation

$F = BIl\sin\theta$

$\theta = 90^\circ$

$F = BIl$

$2BIl$

$F = BI(2l)$

$BIl$

$F_1 = F_2 = BIl$

$1.41\,BIl$

$F^2 = F_1^2 + F_2^2 = 2(BIl)^2$

$a * a + b * b$

The magnetic force depends on the length of the wire.

In $F = BIl\sin\theta$ the length $l$ is a factor. With the same current, field and angle, a wire twice as long feels a force twice as big.

A

The magnetic force depends on the way the wire is bended.

Each short bit of the wire has its own angle $\theta$ to the field, and the force on it is $BI\,\Delta l\sin\theta$ in its own direction. A bend changes these angles and directions, so the total force changes. A straight wire of length $2l$ feels $2BIl$, but the same wire bent into an L feels $\sqrt{2}\,BIl$.

B

The magnetic force depends on the cross-sectional area of the wire.

The area of the cross-section does not appear in $F = BIl\sin\theta$. A thick wire and a thin wire with the same length, current and angle feel the same force.

C

Statement (A) is true, because $l$ is a factor in the force.

Statement (B) is true, because a bend changes the angles and directions of the bits of wire.

Statement (C) is false, because the area is not in the force.

So (A) and (B) are true.

Why the other options fail

A bend changes the force: a straight wire of length $2l$ feels $2BIl$ and the same wire bent into an L feels $\sqrt{2}\,BIl$. So (B) is true as well.

The area of the cross-section is not in $F = BIl\sin\theta$, so (C) is false. And (B) is true.

The length $l$ is a factor in $F = BIl\sin\theta$, so (A) is true. And (C) is false.

The area of the cross-section is not in the force, so (C) is false.

Conclusion

Statements (A) and (B) are true. (C) is false.

The answer is (2).

The quotes give the force on a straight length of wire. For (B) we added the forces on the bits of a bent wire, as vectors, with the L-shape as an example.

Teacher's note

Write $F = BIl\sin\theta$ and ask which quantities are in it.

The length is in it, so (A) is true. The angle of each bit is in it, so the bend matters. The cross-sectional area is not in it.

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