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 what is the mutual inductance

Answer 1

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
`M = 38.2 \ H`

Step-by-step explanation:

From the question we are told that

The number of turns of solenoid 1 is
`N_1 = 800`

The number of turns for solenoid 2 is
`N_2 = 150 \ turns`

The current in the charger is
`I = 220 \ mA = 220 *10^(-3) \ A`

The magnetic flux through solenoid 2 is
`\phi = 0.056 \ Wb`

Generally mutual inductance is mathematically represented as

`M = (N_2 * \phi )/( I )`

=>
`M = (150 * 0.056 )/( 220 *10^(-3) )`

=>
`M = 38.2 \ H`