Question

An insulated wire of diameter 1.0 mm and negligible resistance is wrapped tightly around a cylindrical core of radius 5.0 cm and length 30 cm to build a solenoid. What is the energy stored in this solenoid when a current I = 0.20 A flows through it? (μ0 = 4π × 10-7 T ∙ m/A)

Answer 1

Answer:

5.92 x 10⁻⁵ J

Explanation:

$N$  = Total number of turns

$d$  = diameter of insulated wire = 1 mm = 0.001 m

$l$  = length of the cylindrical core = 30 cm = 0.30 m

Length is given as

$l$ = $N$ $d$

0.30 = $N$ (0.001)

$N$  = 300

$r$ = radius of the core = 5 cm = 0.05 m

Area is given as

$A$ = πr²

$A$ = (3.14) (0.05)²

$A$ = 0.00785 m²

Inductance of the solenoid is given as

$L = \frac{\mu _{o}N^{2}A}{l}$

$L = \frac{(12.56\times 10^{-7}))(300)^{2}(0.00785)}{0.30}$

$L$ = 0.00296

$i$ = current in the solenoid = 0.20 A

Energy stored in the solenoid is given as

$U = (0.5)Li^{2}$

$U = (0.5)(0.00296)(0.20)^{2}$

$U$ = 5.92 x 10⁻⁵ J