Electricity and Magnetism

Topic under the Chapter: Electrostatics

1. Short Introduction

To understand Charge Induction, we need to first know about ‘free electrons’. These free electrons behave very similarly to the gas atoms in a container. Both of them are under continuous random motion throughout the space given to them.

Charge induction forms the working principle behind devices such as capacitors. The understanding that you would obtain by reading this concept would help you see how metals and non-metals behave in practical circuits.

Free electrons are nothing but some loosely bonded valence electrons that come out of the atom very easily, just as the loosely stitched button comes out of the shirt very easily!

Note that :

• A neutral body has an equal number of positive charges and negative charges. The presence of free electrons doesn’t disturb the neutrality of the body, as free electrons are also negative charges, but the only difference is that they are free to move inside the body

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2. Induction in Metal and Non-metals

When we talk of bodies, we classify them as –

• Metals – The ones in which there are a lot of free electrons
• Non-metals – electrons are bound to the Atom tightly (the atom loves them!)

2.1 Charge Induction in Metals

Now suppose you have a metal conductor placed in a region. And you bring a positive charge ‘+q’  in that region ‘externally’.

Important Note : 

• excess of electrons implies negative charge
• A deficiency of electrons implies a positive charge

Text version for Flowchart:

Positive charges exert force on the negatively charged free electrons. Due to this attraction that the electrons feel, they get displaced towards the external positive charge. This causes one region to get an excess of electrons, i.e. negative charge, while the other has a deficiency of electrons, i.e., a positive charge. This is how charge separation happens in a conductor

These charges are ‘induced’ on the conductor due to the external charge. This phenomenon of separation of charges in a body by some external factor is called ‘Charge Induction’

2.2 Charge Induction in Non-Metals

As discussed, the basic difference between non-metal and metals is the absence of free electrons in case of non-metals.

Setup – Let’s consider the same condition. An non-metallic body has been placed in a region. Now, we bring a positive charge in vicinity of this body.

Important Note:

• Atom is made up of a positively charged nucleus and an negatively charged electron cloud surrounding it. In a neutral, undisturbed atom, the negative center and the positive center, both, coincide.

Text version of Flowchart:

Positive charges exert force on the negatively charged electron cloud in the atom.

Due to this attraction, the negative center gets slightly displaced towards the external positive charge.

This causes separation of the negative and positive centers of the atom. We now call this atom a dipole.

All the dipoles tend to align themselves such that the negative side is closer to the external positive charge.

This alignment in dipoles in a non-conducting body due to an external charge is called induction in non-conducting bodies or ‘Polarization’. The separation between positive and negative charges is very very small. So, usually, we ignore it in our problem solving, etc.

Special Note :
This is why a Charged body always attracts a Neutral body. We can also conclude that :
“Attractive force on neutral conducting body will be more due to any external charge”

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FAQ section:

1. What is a Galvanometer?

A galvanometer is a deflection-type meter used to measure current. The needle in the Galvanometer deflects when a current passes through it, and the deflection is proportional to the current.

There are two types of Galvanometers : 

• Uni-Directional
• Bi-Directional

• Unidirectional: In this case, the markings on the dial start at 0 and extend to the maximum range. It has a red terminal, which indicates it must be connected to a high-potential source, and the other is a black terminal for a lower-potential source.

• Bi-Directional: The dial’s zero is in the center, and the maximum is on either side. So, from the direction of deflection, we get to know the direction of current in the conductor, and the amount of deflection gives us the magnitude. 

So, the basic difference between the two is that Unidirectional can give information only about magnitude, while Bi-directional can tell direction as well as magnitude.

The inner setup of a galvanometer has something known as Coil Resistance ‘G,‘ and at maximum deflection, the safe current which flows through the galvanometer is ‘i_g‘. The symbol for a galvanometer is :

Before proceeding, you can cover Series and Parallel Combination

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2. Conversion to Ammeter

The purpose of an Ammeter is also to measure current, but the range for current measurement is much higher. 

• How to Convert? – Just add a resistor with very small resistance (Shunt ‘S’) in parallel to the Galvanometer

What happens because of this?

• Now suppose, ‘I‘ (I > i_g) is the current flowing in the conductor. Since S and G are connected in parallel, ‘I‘ will be divided into ‘i_g‘ and ‘I-i_g‘. 
• The shunt resistance S, being very small in magnitude, will attract a lot of current (since current always prefers the least resistance path). The shunt resistance S is the reason why we are able to supply a larger current than ig.
• This helps us to measure a larger current, resulting in an increase in the range of the galvanometer

How to calculate this ‘I‘?

G and S are in parallel combination

$(I – i_g)\times S = i_g\times G$

From this, find the value of ‘I’. This will give us the maximum safe current allowed into this designed Ammeter

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3. Conversion to Voltmeter

The Voltmeter is used specifically to measure the potential difference across the given terminals.

• How to Convert? – Add a very high ‘Load’ resistance R in series to the Galvanometer

What happens because of this?

Before adding R in series,

$\Delta V = (i_g \times G)$

After adding R in series,

$\Delta V = (i_g \times G) + (i_g \times R)$

The term $(i_g \times R)$ is responsible for the increase in the range of the voltmeter. This enables us to measure larger values. And hence, we need ‘R’ as large as possible.

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4. Examples

Question 1: What shunt resistance is required to make a 1.00 mA, 20 Ω galvanometer into an ammeter with a range of 0 to 50.0 mA?

Solution :

Given:

• Maximum current (I) = 50 mA
• i_g = 1 mA
• G = 20

Solution:

$(I – i_g)\times S = i_g \times G$

By substituting, we get:

$S = 0.408\,\Omega$

Question 2: How can we make a galvanometer with $G = 20\,\Omega$ and $i_g = 1.0\,\text{mA}$ into a voltmeter with a maximum range of 10 V?

Solution :

Given:

• maximum voltage to be measured $\Delta V = 10\,\text{V}$
• $i_g = 1\,\text{mA}$
• $G = 20\,\Omega$

Solution:

For converting a galvanometer to a Voltmeter,

$\Delta V = (i_g \times G) + (i_g \times R)$

By substituting, we get:

$R = 9980\,\Omega$

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Conclusion:

So, we have learnt about the Galvanometer and how we can use it as an Ammeter and a Voltmeter.

• This topic is important not only from a practical point of view but also theory exam point of view
• And other than marks, it’s always good to know about our electrical instruments!

All the Best