Electric Charge
Table of Contents
An electric charge is a fundamental property of matter that describes the amount of electrical energy associated with an object. It is a fundamental property of particles such as protons, electrons, and ions, which are the building blocks of matter.
Electric charge is either positive or negative. Protons carry a positive charge, electrons carry a negative charge, and neutrons have no charge. Objects become charged when there is an imbalance of protons and electrons.
Like charges (positive-positive or negative-negative) repel each other, while opposite charges (positive-negative) attract each other. The unit of electric charge is the coulomb (C), and the amount of charge on an object is measured in coulombs.
Properties of Electric Charge
Here are some properties of electric charge:
- Charge is a fundamental property of matter: Charge is an intrinsic property of subatomic particles such as electrons and protons. It is an essential characteristic of matter that plays a fundamental role in electromagnetism.
- Charge is conserved: Electric charge cannot be created or destroyed. The total amount of charge in a closed system is constant, meaning that charges can only be transferred from one object to another.
- Charge is quantized: Electric charge comes in discrete units, called elementary charges. The elementary charge is the charge of a single electron or proton.
- Charge can be positive or negative: Electric charge can be positive or negative. Protons carry a positive charge, while electrons carry a negative charge.
- Like charges repel, opposite charges attract: Like charges repel each other, while opposite charges attract. This is why positive and negative charges are often referred to as “opposite” charges.
- Charge can be transferred by contact or induction: Electric charge can be transferred from one object to another by contact or induction. Contact occurs when two objects touch, while induction occurs when a charged object creates an electric field that induces a charge on another object without touching it.
- Charge is a source of electric fields: Charged particles create electric fields around them, which can exert forces on other charged particles in their vicinity.
- Charge can flow through conductors: Electric charge can flow through conductive materials, such as metals, due to the movement of electrons. This is the basis for electric current and electrical power.
Numerical Problems on Electric Charge
Here we are providing numerical problems based on electric charge for class 12 physics. problems related to electric charge, types of charges and properties of charge are covered in this article.
Electric Charge Practice Set 1
Apply the quantization of charge formula: $q = \pm ne$Answer: $+1.6 \times 10^{-13}\text{ C}$
Explanation: When electrons are removed, the body acquires a positive charge. We use the quantization of charge formula where $n = 10^6$ and $e = 1.6 \times 10^{-19}\text{ C}$.
Answer: $+1.6 \times 10^{-13}\text{ C}$
Explanation: One million equals $10^6$. Since electrons are removed, the charge becomes positive.
Answer: $-1.6 \times 10^{-14}\text{ C}$
Explanation: Since electrons are negatively charged, adding electrons gives the body a net negative charge. Here $n = 10^5$.
Answer: $-3.2 \times 10^{-10}\text{ C}$
Explanation: Two billion equals $2 \times 10^9$. Because electrons are added, the charge is negative.
Answer: $6.25 \times 10^{18}$ electrons
Explanation: Given the total charge $q = 1\text{ C}$. Rearranging the quantization formula $q = ne$ to solve for $n$:
Answer: (a) $6.25 \times 10^{15}$, (b) $6.25 \times 10^{12}$
Explanation: We know from the previous problem that $1\text{ C}$ corresponds to $6.25 \times 10^{18}$ electrons.
(a) For $q = +1\text{ mC} = 10^{-3}\text{ C}$:
(b) For $q = +1\text{ }\mu\text{C} = 10^{-6}\text{ C}$:
Electric Charge Practice Set 2
Quantization properties and atomic-level charge calculationsAnswer: (a) $12.5 \times 10^{18}$, (b) $31.25 \times 10^{15}$, (c) $2.5 \times 10^{12}$
Explanation: To find the number of electrons, we use $n = |q| / e$.
(a) For $q = -2\text{ C}$:
(b) For $q = -5\text{ mC} = -5 \times 10^{-3}\text{ C}$:
(c) For $q = -0.4\text{ }\mu\text{C} = -0.4 \times 10^{-6}\text{ C}$:
Answer: Yes
Explanation: By the principle of quantization of charge, a body can only possess a charge that is an integral multiple of the elementary charge $e$ ($1.6 \times 10^{-19}\text{ C}$).
Since $n = 30$ is an integer, this charge is physically possible.
Answer: No
Explanation: We test if the charge is an integer multiple of $e$.
Since $n$ is a fraction ($0.3$), and electrons cannot be divided, a body cannot hold this charge.
Answer: (a) Yes, (b) No, (c) No
Explanation: Check if $n = q/e$ results in an integer for each case.
(a) $n = \frac{0.32 \times 10^{-18}}{1.6 \times 10^{-19}} = \frac{3.2}{1.6} = 2$. Since 2 is an integer, Yes.
(b) $n = \frac{0.64 \times 10^{-20}}{1.6 \times 10^{-19}} = \frac{0.064}{1.6} = 0.04$. Not an integer, so No.
(c) $n = \frac{4.8 \times 10^{-21}}{1.6 \times 10^{-19}} = \frac{0.048}{1.6} = 0.03$. Not an integer, so No.
Answer: $99.84 \times 10^{-2}\text{ C}$
Explanation:
Atomic mass of Iron (Fe) $\approx 56\text{ g/mol}$, and atomic number $Z = 26$. Let’s use Avogadro’s number $N_A \approx 6.0 \times 10^{23}$ (simplified for calculation).
1. Mass of iron $m = 224\text{ mg} = 0.224\text{ g}$.
2. Number of moles $= \frac{0.224}{56} = 0.004\text{ moles}$.
3. Total number of atoms $= 0.004 \times (6.0 \times 10^{23}) = 2.4 \times 10^{21}\text{ atoms}$.
4. Total number of electrons $= 26 \times (2.4 \times 10^{21}) = 62.4 \times 10^{21}\text{ electrons}$.
5. Electrons removed ($0.01\%$) $= \frac{0.01}{100} \times (62.4 \times 10^{21}) = 62.4 \times 10^{17}\text{ electrons}$.
6. Total charge $q = ne = (62.4 \times 10^{17}) \times (1.6 \times 10^{-19}) = 99.84 \times 10^{-2}\text{ C}$.
Answer: $1299.2 \times 10^{-2}\text{ C}$
Explanation:
Atomic mass of Copper (Cu) $M \approx 63.5\text{ g/mol}$, and atomic number $Z = 29$.
1. Mass of copper $m = 300\text{ mg} = 0.3\text{ g}$.
2. Number of atoms $= \frac{m}{M} \times N_A = \frac{0.3}{63.5} \times 6.022 \times 10^{23} \approx 2.845 \times 10^{21}\text{ atoms}$.
3. Total number of electrons $= Z \times \text{Number of atoms} = 29 \times (2.845 \times 10^{21}) \approx 8.25 \times 10^{22}\text{ electrons}$.
4. Electrons removed ($0.1\%$) $= \frac{0.1}{100} \times (8.25 \times 10^{22}) = 8.25 \times 10^{19}\text{ electrons}$.
5. Charge $q = ne = (8.25 \times 10^{19}) \times (1.6 \times 10^{-19}) \approx 13.20\text{ C}$.
(Note: The exact answer provided in standard keys, $1299.2 \times 10^{-2}\text{ C}$, may rely on slightly rounded or approximated molar mass constants during intermediate steps, but the operational framework remains $q = \left[ \frac{m}{M} \cdot N_A \cdot Z \cdot \text{fraction} \right] \cdot e$).
