NEET 2022 Physics Magnetic Field in Solenoids MCQ Question

Chapter: Moving Charges and Magnetism

Class: 12 Physics Topic: Magnetic Field Inside a Long Solenoid Difficulty: 🟡 Medium

✅ Ans: $12.56\times10^{-2}\,T$

For a long solenoid:

$$\boxed{B=\mu_0 nI}$$

Given:

• Turns per mm = $100$
• Current $I=1\,A$
• $\mu_0=4\pi\times10^{-7}\,T\,m/A$

Step 1: Convert turns/mm to turns/m

$$100\text{ turns/mm} =100\times1000$$ $$\boxed{n=10^5\text{ turns/m}}$$

Step 2: Put values in the formula

$$B=(4\pi\times10^{-7})(10^5)(1)$$ $$B=4\pi\times10^{-2}$$

Since $4\pi\approx12.56$,

$$\boxed{B=12.56\times10^{-2}\,T}$$

❌ Why other options are wrong?

• $12.56\times10^{-4}T$ → wrong conversion of turns/mm.
• $6.28\times10^{-4}T$ → wrong magnitude.
• $6.28\times10^{-2}T$ → factor of 2 error.

📌 NCERT Concept

For a long solenoid, magnetic field inside is:

$$\boxed{B=\mu_0 nI}$$

where $n=N/L$ is the number of turns per unit length.

The given radius (1 mm) is not required.

🧠 NEET Trick

Whenever you see:

turns/mm → multiply by $10^3$ to get turns/m.

$$100\text{ turns/mm}=10^5\text{ turns/m}$$

Therefore,

$$\boxed{\text{Answer}=12.56\times10^{-2}\,T}$$