Q: Two parallel wires carry equal currents in opposite directions. If a 16-cm wire of mass 14 g is suspended 1.5 mm above a long straight wire, what is the formula for the magnetic force per unit length between the wires?

$$F_{\text{mag}}/L = \frac{\mu_0$ I^2$}{2\pi h}$$

Q: Given the mass $$m = 14\ \text{g}$$ and length $$L = 16\ \text{cm}$$, what is the gravitational force acting on the wire?

$$F_g = m g = 0.014 \times 9.8$$

Q: What is the value of $$\mu_0$, the permeability of free space, used in the calculation of the magnetic force between two wires?

$$\mu_0$ = 4\pi \times 10$$^{-7}$$\ \text{T}\cdot\text{m}/\text{A}$$

Question 1

Two parallel wires carry equal currents in opposite directions. If a 16-cm wire of mass 14 g is suspended 1.5 mm above a long straight wire, what is the formula for the magnetic force per unit length between the wires?

Accepted Answer

$$F_{	ext{mag}}/L = \frac{\mu_0$ I^2$}{2\pi h}$$

Question 2

What physical principle allows the 16-cm wire to 'float' above the long wire with no tension in its suspension leads?

Accepted Answer

The magnetic repulsion between the wires balances the gravitational force.

Question 3

Given the mass $$m = 14\ 	ext{g}$$ and length $$L = 16\ 	ext{cm}$$, what is the gravitational force acting on the wire?

Accepted Answer

$$F_g = m g = 0.014 	imes 9.8$$

Question 4

If the wires are separated by $$h = 1.5\ 	ext{mm}$$, what is the value of $$h in $$meters?

Accepted Answer

$$h = 1.5 	imes 10$$^{-3}$$

Question 5

Which equation must be satisfied for the wire to float with no tension in its suspension leads?

Accepted Answer

$$F_{	ext{mag}} = F_g$$

Question 6

What is the value of $$\mu_0$, the permeability of free space, used in the calculation of the magnetic force between two wires?

Accepted Answer

$$\mu_0$ = 4\pi 	imes 10$$^{-7}$$\ 	ext{T}\cdot	ext{m}/	ext{A}$$

Question 7

If the wire floats, what is the required current $$I in $$each wire, given $$m = 0.014\ 	ext{kg}$$, $$L = 0.16\ 	ext{m}$$, $$h = 1.5 	imes 10$$^{-3}$$\ 	ext{m}$$, and $$g = 9.8\ 	ext{m/s}^2$$?

Accepted Answer

$$I = \sqrt{\frac{2\pi m g h}{\mu_0$ L}}$$

Question 8

Which of the following best describes the direction of the force between two parallel wires carrying currents in opposite directions?

Accepted Answer

The wires repel each other.

Question 9

If the current in both wires is doubled, what happens to the magnetic force between them?

Accepted Answer

The force increases by a factor of 4.

Question 10

A student mistakenly calculates the force using $$F = I B L$$ instead of the correct formula for two parallel wires. What is the main error in this approach?

Accepted Answer

It ignores the mutual interaction and uses the field from only one wire.

Question 11

If the mass of the wire is increased while keeping all other parameters constant, what must happen to the current for the wire to remain suspended?

Accepted Answer

The current must increase.

Question 12

Which real-world application uses the principle of magnetic suspension as described in this problem?

Accepted Answer

Maglev trains

Question 13

If the distance $$h$$ between the wires is halved, what happens to the required current to keep the wire suspended?

Accepted Answer

The required current decreases by a factor of $$\sqrt{0.5}.$$

Question 14

Which of the following is NOT a plausible reason for the wire failing to float as expected in the experiment?

Accepted Answer

The wires are made of non-conductive material.

Question 15

If the wire length is doubled, but all other parameters remain the same, what happens to the required current for suspension?

Accepted Answer

The required current decreases by a factor of $$\sqrt{0.5}.$$

Question 16

Which of the following best describes the relationship between the magnetic force and the distance $$h$$ between the wires?

Accepted Answer

The force is inversely proportional to $$h.$$

Question 17

If the gravitational acceleration $$g is $$increased (e.g., on a planet with higher gravity), what must happen to the current for the wire to remain suspended?

Accepted Answer

The current must increase.

Question 18

Which of the following is a common misconception about the force between two parallel wires carrying current?

Accepted Answer

The force is always attractive regardless of current direction.

Question 19

If the wire is suspended in air, which additional force might need to be considered for a more accurate calculation?

Accepted Answer

Buoyant force due to air

Question 20

Which equation would you use to calculate the magnetic field produced by a long straight wire at a distance $$h$$?

Accepted Answer

$$B = \frac{\mu_0$ I}{2\pi h}$$

Magnetic Suspension: Calculating the Required Current for Floating a Wire

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