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Electric Field & Spherical Symmetry: Assertion & Reason
Introduction
The **electric field** is a fundamental concept in electrostatics, describing how a **charge influences its surroundings**. One of the most crucial properties of a point charge’s electric field is its **spherical symmetry**, meaning its strength is the same at all points equidistant from the charge.
Dependence on Distance
The **electric force** between two charges follows **Coulomb’s Law**:
Dividing by \( q \), we get the **electric field**:
Since **\( E \) depends only on \( r \)**, at all points equidistant from \( Q \), the field is the same in magnitude, proving spherical symmetry.
Assertion-Reason Questions
1. Electric Field on a Sphere
Assertion:
The magnitude of the electric field due to a point charge is the same at all points equidistant from the charge.
Reason:
The electric field follows the inverse square law, depending only on distance.
✅ Answer: Both assertion and reason are true, and the reason explains the assertion.
Since \( E = \frac{Q}{4\pi\epsilon_0 r^2} \), it is the same at all points on a sphere centered at \( Q \). This proves the **spherical symmetry** of a point charge.
2. Inverse Square Law
Assertion:
The electric field of a point charge follows the inverse square law.
Reason:
The electric field is a vector quantity whose direction depends on charge nature.
✅ Answer: Both are true, but the reason does not explain the assertion.
The **magnitude** of \( E \) follows \( E \propto \frac{1}{r^2} \), while the direction depends on charge sign.
3. Spherical Symmetry
Assertion:
The electric field due to a point charge has spherical symmetry.
Reason:
At every point on a sphere centered around the charge, the field has the same magnitude but different directions.
✅ Answer: Both are true, and the reason explains the assertion.
The electric field remains constant in magnitude on a sphere but points radially outward (for \( +Q \)) or inward (for \( -Q \)).
4. Dependence on Test Charge
Assertion:
The electric field at a point depends on the test charge placed there.
Reason:
The test charge is chosen negligibly small to avoid disturbing the source charge.
❌ Answer: The assertion is false, but the reason is true.
The field \( E \) is a property of \( Q \) and **does not depend** on the test charge \( q \).
5. Uniformity of Electric Field
Assertion:
The electric field of a point charge is uniform everywhere in space.
Reason:
The electric field follows an inverse square law.
❌ Answer: The assertion is false, but the reason is true.
The electric field varies with \( r \), meaning it is **not uniform**, but it does follow the inverse square law.
6. Direction of Electric Field
Assertion:
The electric field is radially outward for a positive charge and inward for a negative charge.
Reason:
Electric field lines originate from positive and terminate at negative charges.
✅ Answer: Both assertion and reason are true, and the reason explains the assertion.
Field lines always follow this rule, confirming their direction.
Conclusion
The electric field of a point charge:
- Follows an **inverse square law**.
- Has **spherical symmetry**.
- Is **independent of the test charge**.
- Always **points radially outward (for +Q) or inward (for -Q)**.
Understanding these properties helps in solving problems in electrostatics efficiently.