Electric Charges and FieldsNEET Physics · Class 12 · NCERT Chapter 1

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• Halve r: force becomes 4 times larger (1/r² scaling).
• Set q₁ and q₂ with opposite signs: force becomes attractive (green).
• 1 C is enormous: even 1 μC at 1 cm gives a noticeable force on a similar charge.

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• Doubling r reduces E by a factor of 4.
• Field of 1 μC at 1 cm: about 9 x 10⁷ V/m. Massive.
• Negative q: same magnitude formula but field points TOWARD the charge.

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• Equal and opposite charges (+q and -q): on the perpendicular bisector, E points from + to -.
• Equal positive charges: on the perpendicular bisector, fields combine to point straight away.
• Set the test point right between two equal positive charges: net E = 0.

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• Place the charge inside any shape (cube, sphere, blob), flux is the same Q over epsilon_0.
• Charge OUTSIDE the surface: net flux through it is zero (entering and leaving cancel).
• Negative charge enclosed: net flux is negative (field lines come in).
• 1 μC enclosed: flux about 1.13 x 10⁵ V·m.

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• Infinite line: E falls as 1/r (slower than a point charge).
• Infinite plane: E does NOT depend on distance. Field is uniform.
• Outside a shell: looks just like a point charge at the centre. Like Newton's shell theorem.
• Inside a shell: E = 0 everywhere. The shell provides full electrostatic shielding.

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• At the same r, axial field is exactly twice the equatorial field.
• Both fall as 1/r³, faster than a point charge's 1/r².
• Direction: axial field is along p (from -q to +q). Equatorial is opposite to p.

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• θ = 0° (p parallel to E): torque = 0, U is minimum (stable equilibrium).
• θ = 90° (perpendicular): maximum torque, U = 0.
• θ = 180° (anti-parallel): torque = 0, U is maximum (UNSTABLE equilibrium, tiniest nudge will flip it).
• Work to rotate from θ₁ to θ₂: W = pE(cos θ₁ − cos θ₂).