Table of Contents

**Flux meter:**

Flux meter are used to measure the flux of a permanent magnet so in order to measure the magnet flux surrounded with the permanent magnet. We use a meter called flux meter. The flux meter is actually an advanced form of **ballistic galvanometer**. The advantage of the flux meter is that they require a very low controlling torque and they have heavy electromagnetic damping.

**Construction of the flux meter:**

A flux meter consists of a coil which is freely suspended between the poles of a magnet with the help of spring and a single suspension silk thread. This is the arrangement of the flux meter. There are also certain loose helices and the current enters to this coil. There is no control spring in the flux meter. So there should be some current in this coil. The current enter to the coil through these loose helices and this current will reduce the controlling torque to the minimum value. So we require the controlling torque of a measuring instrument to be minimum. The controlling torque is reduced to a minimum value with the help of this current. The current enter through these helices, the loose helices connected and through this helical structure the current entering is reduce, the controlling torque to the minimum value.

**Working of the flux meter:**

Now we will discuss how to measures the flux associated with permanent magnet. The flux meter measuring the flux linkage associated with permanent magnet. We will connect the flux meter along with a coil which is called search coil. Along with the search coils the terminals of the flux meter will be connected. The flux linkage in this coil is varied by either removing it from the magnetic field or by reversing the field of the magnet. So this coil is placed inside the magnetic field we will first change the magnetic field associated with it or going to reverse the magnetic field and in order to make some flux changes. In order to check whether these changes will be detected by the flux meter or not for this purpose we will change the flux in the search coil. Whenever there are changes in the flux, the search coil an emf or electromotive force will be induced in this coil. Consider the emf induced in the coil is ec and this emf will generate current. This current will be pass through the search coil and also these current will be allowed to pass through the flux meter as they are connected together.

Rf Lf= Resistance and inductance of the search coil

ec= induced emf of the search coil

When the current pass through the flux meter the pointer of the flux meter will deflect and this deflection of the flux meter is directly proportional to the flux linkages. So due to change in the flux linkages the emf is induced and due to which the current is flowing. Whenever the variation of the flux associated with this coil is reduced the pointer deflection will also be reduced and the current will also be reduces. Due to high electromagnetic damping when the flux linkage is reduced the coil will stop movement and the pointer will stop its deflection.

Mathematical form:

According to the Faraday law that the voltage induced in coil is simply equal to the time rate of change of the flux that is in the coil.

V_{((t))=- dΦ/dt
The flux by definition is the integral of the flux density over the area of the coil. The area of the coil consists of the n number of turns. When the flux density is constant across that area then the total flux in the coil then it is given by:
Φ = ∫B.dA
Φ = BA
Φ = NBA}

_{The coils are field sensitive or direction sensitive devices they only measures the direction, the component of the field that is along the axis of the coil. The voltage can be represented as:}

V_{((t))}=- dΦ/dt

V_{((t))}=- dNBA/dt

Since the area of the coil and number of the turns of the coil are constant we can just factor out that we are left with only the time rate of change of flux density. Now integrate both side of the equation in order to eliminate the derivative.

**Ways to use flux meter:**

**Moving coil:**

Moving coil is used to measure the flux change from one area relative to another area.

**Flip the coil:**

As the flux changes from positive to negative we have twice the flux. When we flip the coil and measure that flux change and dividing by two we can find the flux density.

**Moving wire configuration:**

This is used for very narrow gaps when we have to fit the wire through north and South Pole of the magnet only separated by a millimetre where we cannot fit a coil in it. So we use a coil in that case.

**Static coil:**

We can also use static coil this is useful if we have an alternating field, an oscillating field that induces voltage in this static coil.

**Advantages of the flux meter:**

- The flux meter is portable
- They are calibrated directly in weber meter so that we can take directly the reading. So we do not need to convert in other units
- The deflection of the coil free from the time taken by the flux to change. This however time the flux is taking to change its direction or its linkage value. The coil will only consider the flux change. It does not take in to account the time taken
- We can get field map with the help of the flux meter

**Disadvantage:**

- They are less sensitive some it can be inaccurate

**Applications:**

- They are used for measuring the field
- They are used for plotting the hysteresis loop that is hysteresis loop tracers
- They can be used in voltage integration circuits
- Ferromagnetic detectors
- Field surveyors
- Test system in production
- Voltage integration
- Magnetic components quality control
- Dc can be measured
- Magnetic shielding effective errors
- Quality control and development of the magnetic system

**DX201 magnetic flux meter:**

The DX 201 is flux meter which is mostly characterized by the rapid testing induction response and no loss of testing data having design of low drift electronic integrating circuit. The user can measure the samples with pulling method and the test data can nearly be independent from the pulling speed. The repeatability of the tested magnetic flux data is good. DX-102 flux meter is a good integrator which can simulate the circuit design and with the wide application.

**Features: **

- Directly read the magnetic flux data
- It can measures the direction of integration by “-” or “+”.
- The fixtures and integration of coils can be matched with the help of DX 201
- The coil has small effect on the test when the input impedance is high
- The pulse magnetic field can be measured with the help of holding function in the instrument

This device can be adjust stably having low drift, 1µ(Wb/min)

**Ballistic galvanometer:**

A galvanometer is nothing but a PMMC instrument permanent magnet moving coil instrument. Galvanometer is another name of the PMMC instrument. Ballistic galvanometer is a galvanometer which has very little or almost no damping and friction means that it is frictionless and damping fewer instruments. The damping constant for this galvanometer is ideally zero. We can use the fact that the damping is zero to measure the charge flow in short duration during the impulsive current using ballistic galvanometer. A ballistic galvanometer is special type of galvanometer with the help of which we can measures the charge that is flowing in short period of time.

**Ballistic galvanometer Working Principle:**

The working principal of the ballistic galvanometer is based on the deflection of the coil which states that the charge passing through the coil is directly proportional to deflection of the coil. In spite of measuring the current the galvanometer measures the majority of charges passes through the coil.

When a current is passed through a coil suspended freely in a magnetic field, it experiences a force in the direction given by Fleming left hand rule.

**Construction of Ballistic Galvanometer:**

When the charge passes through galvanometer their coil starts rotating and gets an impulse. The impulse of the coil is proportional to the charges passes through it. The actual reading of the galvanometer achieves by using the coil having high moment of inertia.

In ballistic galvanometer we have two magnetic poles which are North and South Pole. A ballistic galvanometer consists of a copper wire coil of large moment inertia, wounded and non-conductive frame. If this coil is wounded on conductive frame then there will be induced current due to which there will be electromagnetic damping. So by using non-conductive frame there will be no induced emf and have no electromagnetic damping. The coil is suspended in a magnetic field by means of a thin phosphor bronze strip which is wounded on non-conductive material.

A concave mirror is rigidly attached to the phosphor bronze strip to record the deflection of the coil by lamp and scale arrangement. The periodic time of the galvanometer should be large as compared to the time for which charge passes. Now the time period of the coil can be represented as:

T=2π √(I/c)

I=(T^{2} c)/4π

Where I represents the moment of inertia, which is directly proportional to the time. The thin phosphor constant “c” value should be keep minimum, the strip should be lengthy and thin so that “c” constant is minimum. When the current flow in the coil and also the coil is placed in the magnetic field so the force will act on it, the sum of the force will be zero because the forces are equal in magnitude but opposite in the direction. Consider the rectangular coil having “N” numbers of turns placed in a uniform magnetic field. Let “l” be the length of and “b” be the breadth of the rectangular coil.

Area of the coil = l × b

When the current is passes through the coil the torque acts on it. The magnitude of the torque acting on the coil is:

T= nILB × b

T= nIB (l× b)

T= nIBA

Let I flow for a small period dt due to which some angular impulse will act on the coil. Now we will find the angular impulse:

T × dt = nIBA × dt

Angular impulse = nIBA × dt

Now if we the current flow for the total time t:

As we know that I= Q/t

Q = It

So we will write the equation in term of charge.

= nBAQ

Where “Q” be the total charge passes through the coil.

Now this is value of the angular impulse with the help of which we can find angular momentum which will act on the coil.

Let ω be the initial angular velocity and I be the moment of the inertia about the suspension.

I_{ω}=nBAq

The angular momentum of the coil can be represented as:

angular momentum=Iω

Iω=nBAq

The force acting on the coil will be equal to the angular momentum.

The coil possess the K.E = 1/2 Iω^{2} at start which entirely used for doing work in twisting the suspension between the initial and final position. In the final position the kinetic energy of the coil is zero.

If c is the restoring couple per unit twist in the suspension then the couple for a twist ɵ is cɵ. The work for an addition twist is dɵ is cɵdɵ. If the maximum angle of twist is ɵ_0 then the total work done against the restoring couple is:

Total work done in twisting the suspension =∫_{0}^{(ɵ0)}cɵdɵ

= (cɵ^{2})/2

ɵ = final twist of the first throw of the coil

Work done in twisting = change in kinetic energy

(cɵ^{2})/2= 1/2 Iω^{2}

Iω^{2} = cɵ^{2}

If “T” is the time period of the calibration of the coil the

Time period of oscillation of coil:

T=2π √(I/c)

I=(T^{2} c)/(4π^{2} )

Now we will multiply on both sides of equation

Iω^{2} × I = cɵ^{2} × I

I^{2} ω^{2} = cɵ^{2} × I

Now we will put the value of I in the above equation and we get:

I^{2} ω^{2} = cɵ^{2} × (T^{2} c)/(4π^{2} )

I^{2} ω^{2} = c^{2} ɵ^{2} × T^{2}/(4π^{2} )

By taking square root on both sides we get:

I^{2} ω^{2} = c^{2} ɵ^{2} × T^{2}/(4π^{2} )

I ω=cɵ T/2π

nBAQ =cɵ T/2π

Q =cɵ T/2πnBA

Q = kɵ where k is equal to c T/2πnBA is a constant and is called the current reduction factor or current required to produce unit deflection. It is also called the constant or ballistic galvanometer or ballistic reduction factor.