Q46E A 15.0-cm-long solenoid with rad... [FREE SOLUTION]

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University Physics with Modern Physics

Hugh D. Young, Roger A. Freedman

Physics

14th edition Edition 路 1596 pages

ISBN: 9780321973610

Chapter 4: Q46E (page 950)

A 15.0-cm-long solenoid with radius 0.750 cm is closely wound with 600 turns of wire. The current in the windings is 8.00 A. Compute the magnetic field at a point near the centre of the solenoid.

Short Answer

Expert verified

The magnetic field at the center of the solenoid is 0.0402T

Step by step solution

Concept of the magnetic field at the center of the solenoid

The magnetic field at the center of the solenoid is given by, $B_{solenoid} = 渭_{0} nl$ $where n = \frac{N}{L} thus, B_{solenoid} = 渭_{0} \frac{N}{L} I were where, 渭_{0} = 4 蟺脳 10^{鈭� 7} H / m$ is permeability of free space, N is the number of turns, I is the current passing through the coil

Find the magnetic field at the center of the solenoid

Consider a solenoid which is L= 15.0 cm long and contains N =600 circular coils R =0.750 cm in radius, it carries a current of I= 8.00 A. The magnetic field at the center of the solenoid is given by, $B_{solenoid} = 渭_{0} \frac{N}{L}$ Substitute the values in the given equation we have,

$\begin{aligned} B_{solenoid} = (4 蟺脳 10^{鈭� 7} Tm / A) (\frac{600}{0.15}) (8.00 A) \\ = 0.0402 T \end{aligned}$