A long solenoid is formed by winding 70 turns cm-1. If 2.0 A current flows, then the magnetic field produced inside the solenoid is _________ (µ0 = 4π × 10-7 TmA-1)
- 1232 × 10–4T
- 176 × 10–4T
- 352 × 10–4T
- 88 × 10–4T
The Correct Option is B
Solution and Explanation
To find the magnetic field inside a solenoid, we can use the formula for the magnetic field inside an ideal solenoid:
\(B = \mu_0 n I\)
Given:
Number of turns per cm = 70turns/cm,
Current I = 2A.
Convert the number of turns per cm to turns per meter (since the SI unit of length is meter):
\(n = 70 \, \text{turns/cm} \times 100 \, \text{cm/m} = 7000 \, \text{turns/m}\)
\(B = \mu_0 n I\)
\(B = (4\pi \times 10^{-7} \, \text{T m/A}) \times (7000 \, \text{turns/m}) \times (2 \, \text{A})\)
\(B = 4\pi \times 10^{-7} \times 7000 \times 2\)
\(B = 4\pi \times 14000 \times 10^{-7}\)
\(B = 56000\pi \times 10^{-7}\)
\(B = 5.6\pi \times 10^{-3} \, \text{T}\)
\(B = 5.6 \times 3.14 \times 10^{-3} \, \text{T}\)
\(B = 17.584 \times 10^{-3} \, \text{T}\)
\(B = 0.0176 \, \text{T}\)
\(B = 176 \times 10^{-4} \text{T}\)
So, the correct option is (B): \(176 \times 10^{-4} \text{T}\)
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Concepts Used:
Magnetism & Matter
Magnets are used in many devices like electric bells, telephones, radio, loudspeakers, motors, fans, screwdrivers, lifting heavy iron loads, super-fast trains, especially in foreign countries, refrigerators, etc.
Magnetite is the world’s first magnet. This is also called a natural magnet. Though magnets occur naturally, we can also impart magnetic properties to a substance. It would be an artificial magnet in that case.
Read More: Magnetism and Matter
Some of the properties of the magnetic field lines are:
- The lines and continuous and outside the magnet, the field lines originate from the North pole and terminate at the South pole
- They form closed loops traversing inside the magnet.
- But here the lines seem to originate from the South pole and terminate at the North pole to form closed loops.
- More number of close lines indicate a stronger magnetic field
- The lines do not intersect each other
- The tangent drawn at the field line gives the direction of the field at that point.