# Multiturn coil induced voltage

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#### Darius Baronas

##### Member level 3 Hi ! I made multi-turn air cored coil myself. I know that the coil is in the magnetic field that changes 8Hz frequency, magnetic field density is 0.5 T. How mathematically calculate induced voltage in a coil ? Can't find any information with equations.. Thanks !

#### FvM

##### Super Moderator
Staff member I presume you'll find the equation in your physics or electrical engineering text book. It's also derived here https://en.wikipedia.org/wiki/Electromagnetic_induction

For 8 Hz sinusoidal flux density with Bpk = 0.5 T peak, you get

Vpk = 2pi*8*0.5*n*A, n = number of turns, A = coil area [m²]

#### Darius Baronas

##### Member level 3 And here no matter that my coil is from 0.2mm diameter wire and 5mm in a length ?

##### Super Moderator
Staff member There are the right and left hand rules which relate magnetic flux to current flow through wires.

John Ambrose Fleming is credited with discovering this rule.

From:
https://en.wikipedia.org/wiki/Fleming's_left-hand_rule_for_motors

"Fleming's left-hand rule is used for electric motors, while Fleming's right-hand rule is used for electric generators."

Also see:
https://en.wikipedia.org/wiki/Right-hand_rule

How mathematically calculate induced voltage in a coil ?

This is not necessarily easy to measure, or to calculate.

Current is induced in the inductor. It can only flow if the inductor sees finite impedance. The developed voltage is generated by the inductor. The inductor produces whatever voltage is necessary, in order to ensure Ampere flow through the impedance.

The only time you can measure this voltage directly, is when all external voltages are zero.

#### D.A.(Tony)Stewart Do you care about inter winding capacitance , SRF and Q of inductor?

#### volker@muehlhaus Do you care about inter winding capacitance , SRF and Q of inductor?

Do you think that makes a big difference at f=8 Hz?

#### Darius Baronas

##### Member level 3 I know that is easier to measure. I measured, that Voc @8Hz is 880mV ( 1,76 V peak to peak) . I need to make calculations and compare that with measured value..

#### D.A.(Tony)Stewart Do you think that makes a big difference at f=8 Hz?

H actually said changes 8 Hz.. From what?

#### Darius Baronas

##### Member level 3 Here is my generator: Every second magnet is reversed direction, so when motor speed is 1 rotation per second, we have 8Hz magnetic flux change. So i want to calculate induced voltage in SINGLE coil (in the picture there are 5) . I measured that the voltage is about 880mV. I need to show that with calculation..

#### FvM

##### Super Moderator
Staff member And here no matter that my coil is from 0.2mm diameter wire and 5mm in a length ?
It won't for a homogenous 0.5T field. But looking at the photo, the field is far from being homogenous. And neither sinusoidal in time.

As mentioned in your previous thread https://www.edaboard.com/threads/328374/, it's a 3D AC magnetics problem that can't be easily simulated. The calcuculation in post #2 gives a best at ballpark figure.

#### Darius Baronas

##### Member level 3 Maybe you have link from what source is that #2 post equation ? I want to read more about it

#### FvM

##### Super Moderator
Staff member Maybe you have link from what source is that #2 post equation ?
Any experimental physics text book.

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