EXMMPLE 8.1: MAGNETIC FIELD OF A SOLENOID A student takes a long straight copper wire (with insulation on it) from his phyiks tab, hews the wire on an iron rod of 50 cm , to make it solenoid of [55 (ums. He connects the ends or on w wife with the battery, which provides 1.2 A current. Find the magnetic field he profent solenoid by doing so.
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To find the magnetic field inside a solenoid, you can use the formula \( B = \mu_0 \times n \times I \), where \( B \) is the magnetic field, \( \mu_0 \) is the permeability of free space (\( 4\pi \times 10^{-7} \, T \cdot m/A \)), \( n \) is the number of turns per unit length, and \( I \) is the current. In this case, the student has a solenoid with 55 turns and a length of 50 cm (0.5 m). Thus, \( n = \frac{55 \, turns}{0.5 \, m} = 110 \, turns/m \). Plugging in the numbers: \[ B = (4\pi \times 10^{-7}) \times 110 \times 1.2 = 1.57 \times 10^{-4} \, T \] So, the magnetic field inside the solenoid is approximately \( 1.57 \times 10^{-4} \, T \). Ever wondered how powerful a solenoid can actually get? When you increase either the current or the number of turns, you massively boost the magnetic field strength! It’s like putting a turbocharger on your favorite toy car—watch it zoom! Just remember, safety first: high currents can heat wires; use caution when experimenting. Now, if you're curious to dive deeper into the world of electromagnetism, check out "Introduction to Electrodynamics" by David J. Griffiths. It’s a classic that gives you a solid foundation and makes students fall in love with electric and magnetic fields! Whether you're preparing for exams or just want to impress friends, this book's got you covered!
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