⚡Electric Fields
What is an Electric Field?
An electric field is a region of space where an electric force acts on charged objects. It's a way of describing how a charge affects the space around it, without needing a second charge present.
E = F/q₀
Where q₀ is a small positive "test charge" placed at that location.
For a single point charge Q: E = kQ/r²
Electric field is a vector pointing: - Away from positive charges (they'd push a positive test charge away) - Toward negative charges (they'd pull a positive test charge inward)
Units: N/C (Newtons per Coulomb)
Electric Field Lines
Electric field lines visualize the field: - Point from + to − - Closer lines = stronger field - Never cross - Perpendicular to conductor surfaces
The force on a charge q in a field E: F = qE
If q is positive, force is in the direction of E. If q is negative, force is opposite to E.
✏️ Worked Example
Problem: A proton (q = 1.6×10⁻¹⁹ C) is placed in a uniform electric field E = 500 N/C. Find the force and acceleration. (m_p = 1.67×10⁻²⁷ kg)
📐 Key Equations
Electric Fields
E⃗ = \fracF⃗q_0 = (kQ)/(r²)r̂F = qE⚠️ Common Mistakes
Misconception: The electric field direction is always away from the source charge.
✓ Correct thinking: The electric field points AWAY from positive source charges and TOWARD negative source charges.
Why: The field direction is defined as the direction of force on a positive test charge. A positive test charge is repelled by +Q and attracted by −Q.
Misconception: A negative charge placed in a field E moves in the direction of E.
✓ Correct thinking: A negative charge experiences a force OPPOSITE to E (F = qE, and q is negative, so F is anti-parallel to E).
Why: Field lines show the direction of force on a positive test charge. Any negative charge is pushed the other way.
Misconception: A stronger electric field means more charges nearby.
✓ Correct thinking: Field strength depends on both the source charge magnitude AND the distance squared: E = kQ/r². A small charge very close can create a stronger field than a large charge far away.
Why: The 1/r² distance dependence can dominate. Field lines drawn closer together represent a stronger field, regardless of source charge.
📝 Practice Problems
Try these problems. Check your answer when ready.
A charge Q = +5 μC creates an electric field at a point 0.3 m away. Find E.
E = (kQ)/(r²)A proton is placed in an electric field E = 2000 N/C. Find the force on it and its acceleration. (m_p = 1.67×10⁻²⁷ kg)
At what distance from a +3 μC charge is the electric field equal to 1.2×10⁶ N/C?
An electron (charge −e, mass 9.11×10⁻³¹ kg) is placed in a uniform electric field E = 3000 N/C pointing right. Find the magnitude and direction of its acceleration.
Two charges: +Q at x = 0 and −Q at x = d. Find the electric field at the midpoint x = d/2 (magnitude and direction).
A small ball of mass 0.002 kg and charge +4 μC is suspended in equilibrium in a uniform electric field. If gravity acts downward, what electric field (magnitude and direction) is needed to suspend the ball?
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