Complete Question
Suppose a wireless charging system of an electric toothbrush. The charger has Solenoid 1 with 800 turns and the toothbrush has Solenoid 2 with 150 turns. The current in the charger is 220 mA and the corresponding average magnetic flux through Solenoid 2 is 0.056 Wb. What is the mutual inductance of the pair of the solenoids?
Answer:
The value is [tex]M = 38.2 \ H[/tex]
Explanation:
From the question we are told that
The number of turns of solenoid 1 is [tex]N_1 = 800[/tex]
The number of turns for solenoid 2 is [tex]N_2 = 150 \ turns[/tex]
The current in the charger is [tex]I = 220 \ mA = 220 *10^{-3} \ A[/tex]
The magnetic flux through solenoid 2 is [tex]\phi = 0.056 \ Wb[/tex]
Generally mutual inductance is mathematically represented as
[tex]M = \frac{N_2 * \phi }{ I }[/tex]
=> [tex]M = \frac{150 * 0.056 }{ 220 *10^{-3} }[/tex]
=> [tex]M = 38.2 \ H[/tex]
