# Magnetic Flux and Voltage: 7 Interesting Facts

In this article, the topic, “Magnetic Flux and Voltage” with 7 interesting facts will be discussed in a brief manner and trying to clarify the topic. Magnetic flux and magnetic field both are the different term.

From the law of the Faraday’s the concept of magnetic flux and voltage clearly can be get. When a convolution of wire is passes by a field of magnetic in this particular case voltage is produce which depend upon the magnetic flux via the surface of the convolution.

The meaning of the term of magnetic field is a particular region in where the force of the magnetic can be observed. In the other hand the meaning of the term magnetic flux is, the net amount of field of magnetic can passes through a specified area.

## How does voltage affect magnetic flux?

When in a surface area a magnet is placed at this place magnetic field is present. A body which is already magnetically active or a charge which have already movement in this case field o the magnetic can be observed.

The property magnetic flux is not directly depend upon the property of voltage, but with current magnetic flux is directly connected. The law of OHM shows that current has a deep relation with voltage and resistance. The magnetic flux and voltage is directly proportional to each other.

The formula for the magnitude of the magnetic field can be written as,

B = \frac{\mu_0I}{2\pi r} ….eqn (1)

In this formula the expressions are,

B is denoted as, the magnitude of the magnetic field and unit is Tesla.

\mu_0 is denoted as, permeability of free area and unit is Tesla meter per ampere

I is denoted as, magnitude of the electric current and unit is Ampere.

r is denoted as, Distance of separation and unit is meter.

The formula shown us, field of the magnetic is directly proportional with the property of current.

We also know that,

V = IR ….eqn (2)

I = \frac{V}{R}….eqn (3)

In this formula the expressions are,

I = Current

V = Voltage

R = Resistance

From the ….eqn (3) we can observe that, current (I) is directly proportional with the property of voltage (V).

Comparing the ….eqn (1) and ….eqn (3) we can write,

B = \frac{\mu_0 I}{2\pi r}

B = \frac{\mu_0 V}{2\pi R} ….eqn (4)

Eqn (4) clearly shows that field of the magnetic are directly proportional with the voltage. We know, magnetic flux is, the net amount of field of magnetic can passes through a specified area. Since, magnetic flux is also directly proportional with the voltage. Means if the value of magnetic flux is increases then the value of current is also increases and if the value of magnetic flux is decreases then the value of current is also decreases.

In the other hand the relationship with the resistance and magnetic field is inversely proportional with each other. Means if the value of magnetic flux is increases then the value of resistance is decreases and if the value of magnetic flux is decreases then the value of resistance is increases.

## Relationship between magnetic flux and induced voltage:

The induced voltage can be explain as, the changing of motion of the property of magnetic flux via a circuit which is closed.

The relationship with the property of magnetic flux and induced voltage is directly proportional to each other. Means if the value of magnetic flux is increases then the value of induced current is also increases and if the value of magnetic flux is decreases then the value of induced current is also decreases.

### The formula for the Induced voltage:-

The formula expression for the induce voltage is given below,

\epsilon = – N \frac{d\phi_B}{dt}

Where,

\epsilon is pointed as induced voltage

N is pointed as the net digit of turns of the loop

\phi_B is pointed as magnetic flux

\phi_B can be also written as,

\phi_B = B\times A

Where,

B is pointed as field of magnetic

A is pointed as surface of the loop

t is pointed as taken time

The induced voltage is denoted as the symbol of \epsilon. The dimensional expression for the induced voltage is ML^2A^-^1T^-^3.

The unit is used to measure the parameter of induced voltage is volts (V).

From the formula of the induced voltage we get a clear relationship in between the net digit of turns of the loop, surface of the loop and surface of the loop with the induced voltage is directly proportional to each other. And the relationship with the time and induced voltage is inversely proportional with each other.

## How is magnetic flux used to create a voltage?

When a coil of wire is moved via a field of the magnetic a voltage is generated which depends on the magnetic flux by the surface of the coil. This is described by law of the Faraday.

A voltage is induced in the coil when a bar magnet is pushed in and pushed out of it. Voltages of opposite signs are generated by rate in opposite point of the compass and the voltages are also reversed by reversing poles.

## How to calculate magnetic flux from voltage:

The magnetic flux is determine from the voltage with the help of this expression,

\epsilon = – N \frac{d\phi_B}{dt}

Where,

\epsilon is pointed as induced voltage

N is pointed as the net digit of turns of the loop

\phi_B is pointed as magnetic flux

\phi_B can be also written as,

\phi_B = B\times A

Where,

B is pointed as field of magnetic

A is pointed as surface of the loop

t is pointed as taken time

Simply the values which are known, just putting them, and easily can estimate the value of magnetic flux from it.

The magnetic flux is determine from the voltage with the some numerical problem it is describe below,

### Problem:-1

In a coil have the number of turns is 10 and magnetic flux in that area is 6.5 Tesla per meter square. The time taken for completing the process is 6 second.

Now determine the amount of induced voltage in that area.

Solution:-

Given data are,

The number of turns for the coil is = 10

Time taken (dt) = 6 second

Magnetic flux in that area (d\phi)= 6.5 Tesla per meter square

We know that,

The formula expression for the induce voltage is given below,

\epsilon = – N \frac{d\phi_B}{dt}

Where,

\epsilon is pointed as induced voltage

N is pointed as the net digit of turns of the loop

\phi_B is pointed as magnetic flux

dt is pointed as taken time

Putting the values,

\epsilon = – N \frac{d\phi_B}{dt}

\epsilon = 10\frac{6.5}{6}

\epsilon = 10.83 V

In a coil have the number of turns is 10 and magnetic flux in that area is 6.5 Tesla per meter square. The time taken for completing the process is 6 second.

So, the amount of induced voltage in that area is 10.83 volts.

### Problem:-2

In a coil have the number of turns is 10 and magnetic flux in that area is 2.5 Tesla per meter square. The time taken for completing the process is 3 second.

Now determine the amount of induced voltage in that area.

Solution:-

Given data are,

The number of turns for the coil is = 10

Time taken (dt) = 3 second

Magnetic flux in that area (d\phi) = 2.5 Tesla per meter square

We know that,

The formula expression for the induce voltage is given below,

\epsilon = – N \frac{d\phi_B}{dt}

Where,

\epsilon is pointed as induced voltage

N is pointed as the net digit of turns of the loop

\phi_B is pointed as magnetic flux

dt is pointed as taken time

Putting the values,

\epsilon = – N \frac{d\phi_B}{dt}

\epsilon = 10\frac{2.5}{3}

\epsilon = 8.33 V

In a coil have the number of turns is 10 and magnetic flux in that area is 2.5 Tesla per meter square. The time taken for completing the process is 3 second.

So, the amount of induced voltage in that area is 8.33 volts.

## Magnetic flux and voltage graph:

A change in flux induces a current and a voltage which is directly proportional to the rate of change of flux.

## Does magnetic flux increase with voltage?

Magnetic flux increases with voltage this relationship fits with Ohm’s law. A current and a voltage in a closed coil generate a flux which is proportional with current and voltage.

Yes magnetic flux increases with the voltage. In a closed circuit the motion of change for the magnetic flux is directly proportional with the voltage of that particular closed circuit in a fixed time period. The faster changes of the motion of field of the magnetic means the greater quantity of voltage in a closed circuit.

### The difference between the magnetic flux and magnetic field:-

The major difference in between the magnetic flux and magnetic field are discussed below,

## Problem statement with solution:-1

In a coil have the number of turns is 15 and magnetic flux in that area is 4.5 Tesla per meter square. The time taken for completing the process is 6 second.

Now determine the amount of induced voltage in that area.

Solution:-

Given data are,

The number of turns for the coil is = 15

Time taken (dt) = 6 second

Magnetic flux in that area (d\phi) = 4.5 Tesla per meter square

We know that,

The formula expression for the induce voltage is given below,

\epsilon = – N \frac{d\phi_B}{dt}

Where,

\epsilon is pointed as induced voltage

N is pointed as the net digit of turns of the loop

\phi_B is pointed as magnetic flux

dt is pointed as taken time

Putting the values,

\epsilon = – N \frac{d\phi_B}{dt}

\epsilon = 15\frac{4.5}{6}

\epsilon = 11.25 V

In a coil have the number of turns is 15 and magnetic flux in that area is 4.5 Tesla per meter square. The time taken for completing the process is 6 second.

So, the amount of induced voltage in that area is 11.25 volts.

## Problem statement with solution:-2

In a coil have the number of turns is 22 and magnetic flux in that area is 5.4 Tesla per meter square. The time taken for completing the process is 6 second.

Now determine the amount of induced voltage in that area.

Solution:-

Given data are,

The number of turns for the coil is = 22

Time taken (dt) = 6 second

Magnetic flux in that area (d\phi) = 5.4 Tesla per meter square

We know that,

The formula expression for the induce voltage is given below,

\epsilon = – N \frac{d\phi_B}{dt}

Where,

\epsilon is pointed as induced voltage

N is pointed as the net digit of turns of the loop

\phi_B is pointed as magnetic flux

dt is pointed as taken time

Putting the values,

\epsilon = – N \frac{d\phi_B}{dt}

\epsilon = 22\frac{5.4}{6}

\epsilon = 19.8 V

In a coil have the number of turns is 22 and magnetic flux in that area is 5.4 Tesla per meter square. The time taken for completing the process is 6 second.

So, the amount of induced voltage in that area is 19.8 V.

#### Conclusion:-

Magnetic flux and voltage proportional to each other.