A solenoid with 1000 turns has a cross-sectional area of 7.0 cm² and length of 25 cm.How much energy is stored in the magnetic field of the solenoid when it carries a current of 10.0 A?
A)0.10 J
B)2.8 J
C)0.18 J
D)28 J
E)0.36 J

Question

Quizplus · Accepted Answer

The energy stored in the magnetic field of a solenoid can be calculated using the formula: $E = \frac{1}{2}LI^2$, where $E$ is the energy in joules, $L$ is the inductance of the solenoid in henries, and $I$ is the current in amperes. The inductance $L$ of a solenoid is given by $L = \mu_0N^2A/l$, where $\mu_0$ is the permeability of free space ($4\pi \times 10^{-7}$ Tm/A), $N$ is the number of turns, $A$ is the cross-sectional area in square meters, and $l$ is the length of the solenoid in meters.Given:- $N = 1000$ turns,- $A = 7.0 \, \text{cm}^2 = 7.0 \times 10^{-4} \, \text{m}^2$,- $l = 25 \, \text{cm} = 0.25 \, \text{m}$,- $I = 10.0 \, \text{A}$.First, calculate the inductance $L$:$$L = \frac{4\pi \times 10^{-7} \times (1000)^2 \times 7.0 \times 10^{-4}}{0.25} = 3.5 \times 10^{-3} \, \text{H}$$Then, calculate the energy $E$:$$E = \frac{1}{2} \times 3.5 \times 10^{-3} \times (10.0)^2 = 0.175 \, \text{J}$$Rounded to two significant figures, the energy stored is $0.18 \, \text{J}$, which corresponds to choice C.

A Solenoid with 1000 Turns Has a Cross-Sectional Area of 7.0