Verified Solution • 2025–26 Session moderate

QPages 249-253: Q56: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Due to a Current Pages 249-253: Q56 Solution: A copper wire having resistance 0.01 ohm in each metre is used…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often multiply the resistance per metre by the radius or a single turn instead of the full wire length $l=2\pi r N$, causing the calculated emf to be wrong; always compute $R=(\text{Ω/m})\times(2\pi r N)$ before using $V=IR$.

A copper wire having resistance 0.01 ohm in each metre is used to wind a 400-turn solenoid of radius 1.0 cm and length 20 cm. Find the emf of a battery which when connected across the solenoid will cause a magnetic field of

1.0 \times 10^{-2} \text{ T}

near the centre of the solenoid.

Step-by-Step Verified Solution

**Answer:**

\varepsilon = 1.6

V. **Step-by-Step Explanation:**

N = 400

,

r = 0.01

m,

L = 0.2

m,

B = 10^{-2}

T.

n = N/L = 2000

turns/m.

i = \frac{B}{\mu_0 n} = \frac{10^{-2}}{4\pi \times 10^{-7} \times 2000} = 3.98

A. Resistance =

0.01 \times 2\pi r \times N = 0.01 \times 2\pi \times 0.01 \times 400 = 0.25

�.

\varepsilon = iR = 3.98 \times 0.25 = 1

V.

All Questions in this Chapter

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