Electric Fields and Capacitance

• Electric fields exist around objects, exerting an electric force on other charges within them.
• The electric field created by a point charge -Q (where Q>0) points towards the charge.
• Electric lines of force indicate the direction of the electric force acting on a point charge.
• Diagram b depicts the electric field of uniform charge.
• Air cannot be used as a capacitor
• The work done by an electric force on a point charge q moving from point M to N in an electric field does not depend on the path taken.
• The potential energy of a charge q in an electric field characterizes the ability of the electric field to do work.
• Three capacitors, each with a capacitance of 3µC, connected in parallel yield a total capacitance of 9µC.
• If W is the electrostatic potential energy of a test charge q, the electric potential V at the point where the test charge is placed is V = W/q.
• If two charged spheres A and B are separated by a distance r in air, the diagram shows that q1 is negative and q2 is positive.
• If the potential at point M is 0 V, then the potential at N is -20 V.
• When a potential difference U is applied across two parallel metal plates separated by a distance d, the electric field strength between the plates is E. If the distance remains constant, but the potential difference increases by a factor of 3, the electric field strength between the two plates increases by a factor of 3.
• The formula to calculate the electric field strength at a point located at a distance r from a point charge Q is E = Q / (4πε₀r²).
• The SI unit of capacitance is the Farad (F).
• A small charged sphere is suspended between two parallel metal plates with opposite charges. To balance the sphere, the electric field must be oriented vertically upwards.

True/False Questions

• A positive point charge (q>0) released with no initial velocity moves a distance s (cm) along a line of force of a uniform electric field with strength E (V/m).
• A uniform electric field has different strengths at different points in the field.
• The charge moves along the direction of the electric force (same direction).
• The work done by the electric field depends on the shape of the trajectory.
• If q = 2.10⁻⁶C, the magnitude of the electric field is 5000V/m, and the displacement of the charge is 5cm, then the work done by the electric force is 5.10⁻⁵J.

Short Answer Questions

• When a charge q = -2C moves from point M to point N in an electric field, the electric force generates -6J of work. The electric potential at M is 3 Volts (V) higher than at N.
• An electron is released with no initial velocity near the negative plate in a uniform electric field between two parallel metal plates with opposite charges. The electric field strength between the plates is 1000 V/m, and the distance between the plates is 1 cm. The kinetic energy of the electron when it hits the positive plate is a.10⁻¹⁸J, where a = 1.6.

Free Response Questions

• A right triangle ABC with a right angle at A is placed in a uniform electric field E, where α = ABC = 60°, and AB is antiparallel to E. Given BC = 6cm and UBC = 120V:
  • Find UAC, UBA, and the electric field strength E.
  • Calculate the work done by the electric field when a charge q = -4.10⁻⁶C is moved from A to B, B to C, and C to A. Note: The answers should be UAC = 72V, UBA = 48V, E = 2400 V/m; A(A->B) = 192.10⁻⁶ J, A(B->C) = -288.10⁻⁶ J; A(C->A) = 96.10⁻⁶ J
• Two charges, q₁ = q₂ = 4.10⁻¹⁰C, are placed at points A and B in a vacuum, separated by 4cm. Determine the electric field vector at point M, where MA = 1cm and MB = 3cm. Also, find the location of point H where the electric field strength is zero.