Two parallel conductors carrying currents $I_1$ and $I_2$ expe... | General Science MCQ | Examoogle

General SciencePhysics: Electromagnetism

Two parallel conductors carrying currents $I_1$ and $I_2$ experience a force of 4 N. If both currents are tripled and the distance between them is doubled, what is the new force?

18 N

9 N

24 N

6 N

Correct Answer

🔬 SC • Science Concept & PrincipleGeneral SciencePhysics: Electromagnetism

Option A

18 N

Quick Summary:

The magnetic force per unit length between two parallel conductors is directly proportional to the product of the currents and inversely proportional to the distance between them. By scaling the variables, we determine that the new force is 18 N.

🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Think of it like magnets: making the magnets 3 times stronger each increases their pull significantly, but pulling them twice as far apart weakens that combined pull.

🧠 Memory Mnemonic / Shortcut Aid

F-I-I-r: Force is proportional to product of Currents (I, I) over radius (r).

🔢 Key Formulas

$F = \frac{\mu_0 I_1 I_2 L}{2 \pi r}$ — Force between two parallel current-carrying conductors

$F' = F \left( \frac{I_1'}{I_1} \cdot \frac{I_2'}{I_2} \cdot \frac{r}{r'} \right)$ — Scaling factor for the force

⚙️ Working Principle

The magnetic force $F$ between two parallel wires of length $L$ separated by distance $r$ is given by $F = \frac{\mu_0 I_1 I_2 L}{2 \pi r}$ . When $I_1$ and $I_2$ are tripled (becoming $3I_1$ and $3I_2$ ) and $r$ is doubled (becoming $2r$ ), the new force $F'$ becomes $F' = F \times \frac{3 \times 3}{2} = 4.5 \times F$ . Given the initial force $F = 4 \text{ N}$ , the new force is $4.5 \times 4 = 18 \text{ N}$ .

📌 Key Points

▸
Magnetic force is attractive for currents in the same direction and repulsive for opposite directions.
▸
The force magnitude depends linearly on both currents.
▸
The force magnitude follows an inverse relationship with distance.

✅ Advantages

▸
Useful for defining the standard unit of current, the Ampere.

❌ Disadvantages / Limitations

▸
Requires high precision measurements due to small force magnitudes at typical laboratory scales.

🛠️ Applications / Uses

▸
Electromagnetic motor design
▸
Power transmission line stress calculation

📄 Additional Information

▸
The permeability constant is $\mu_0 = 4 \pi \times 10^{-7} \text{ T m/A}$ .
▸
Option B (9 N) is a common error resulting from failing to account for the distance change.

📊 Diagram / Illustration

✅

A is correct — The force scales by a factor of 4.5, resulting in 18 N when the initial force is 4 N.

Core Concepts Used

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Ampere's Law Lorentz Force Magnetic Field of a Solenoid

💡 EXAM TIP

When scaling problems appear in physics, always identify the proportionality constant or ratio first to avoid long-form calculation errors.

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