Question

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 × 10−2 T near the centre of the solenoid.

Answer 1

Explanation:

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Answer 2

Explanation:

Step 1:

Given data in the question  :-

Pro unit length resistance of the wire R/l= 0.01 Ω/m

Radius wire, r = 1.0 cm = 0.01 m

number of turns, N = 400

Magnetic field strength , B = 1.0 × 10−2 T

Step 2:

Let E be the battery emf, and let $R_0$ be the minimum wire resistance.

$i= \frac{E}{ R_0} = \frac{E}{(0.01 \times 2\pi r \times 400)}$

$= \frac{E}{ (0.01\times 2\pi \times 0.01 \times 400)}$

Step 3:

The magnetic field around the solenoid core is imparted by

$B= \mu_0 ni$

=$1\times 10^{-2} = 4\pi \times 10^{-7} \times \frac{ 400}{(20 \times 10^{-2} )} \times \frac{E}{ (2\pi \times 4 \times 10^{-2} )}$

$E= \frac{( 10^{-2} \times 20 \times 10^{-2} \times 2 \times 10^{-2} )}{(10^{-7} \times 4 \times 10^{2} )}$

 E = 1 V