Revision summary

State the source, test charge, direction and reference. Then select a force, field, potential or energy equation appropriate to that quantity.

Point charges: signs and inverse powers

These point-charge equations use free space or air and centre separation r. Like signs repel and unlike signs attract. The source determines E and V; test-charge sign then determines its force and pair energy. Potential is scalar, while fields and forces add as vectors.

Potential is external work per unit small positive test charge brought from infinity without a kinetic-energy change. With the isolated-source zero at infinity, V follows source sign and U_E follows the product of the two signs.

The work and motion statements require the stated fixed-source, negligible-other-transfer conditions. Moving -2.00 nC from +120 to +60.0 V raises its pair energy by +1.20 × 10^-7 J.

Use a local gradient and a perpendicular gap

A tangent slope of -400 V/m gives a +400 N/C component. A chord across a finite interval need not give that local value. Field is perpendicular to equipotentials and points towards decreasing V; a negative charge's force is opposite E.

At the midpoint between two equal positive sources, fields can cancel while potentials add. With equal opposite sources, potentials can cancel while fields reinforce. Zero E and zero V are different conditions.

For plates at +120 and 0 V separated by 0.0300 m, the field is 4000 V/m from the higher to lower potential. Use the perpendicular gap, not plate length. A chosen 0 V label does not imply an Earth connection.

Calculate motion in components

With electric force alone, a = qE/m. An electron is accelerated opposite E. In the supplied transverse-entry model, x = u_xt and y = (1/2)a_yt², with v_x unchanged. Transit is 3.00 ns, exit deflection is 3.16 mm and exit v_y is 2.11 × 10⁶ m/s upward. This is inside the 15.0 mm half-gap.

After the ideal field ends, force-free motion follows the exit tangent. It does not continue curving or reset to horizontal. Revisit the component graphs and energy check to connect the exit state to its assumptions.

Capacitor charge, graph axes and constraints

Q is the magnitude on either plate. Opposite charges +Q and -Q give zero net pair charge while storing charge separation. Constant C describes a linear capacitor within its operating range.

Q against V has gradient C. V against Q has gradient 1/C, and its area gives stored energy. For the 10.0 microfarad, 12.0 V model, Q = 120 microcoulombs and U = 0.720 mJ.

• Same C, doubled V: Q doubles and U quadruples.
• Same V, doubled C: Q and U double.
• Same Q, doubled C: V and U halve.

State whether a source maintains V or an isolated, non-leaking capacitor retains Q. In the specified initially uncharged, constant-voltage resistive charging model, source transfer V_sQ exceeds the final stored energy; account for energy transferred in the resistance.

Quantities and units

Use 10^-9 for nano, 10^-6 for micro and 10^-3 for milli. Here E means field; energy is U or E_k. The letter C can mean capacitance as a quantity or coulomb as a unit, while F can mean force as a quantity or farad as a unit.