Electrostatics Test. 2

Use the energy formula for a capacitor: U = 0.5 * C * V². Convert capacitance to Farads: C = 200 x 10⁻⁶ F. Then, U = 0.5 * (200 x 10⁻⁶ F) * (50 V)² = 0.5 * (200 x 10⁻⁶) * 2500 = 0.25 J.

The force on a charge is F = qE. Since an electron's charge (q) is negative, the force vector will be in the opposite direction to the electric field vector.

The potential inside a charged conductor is constant and equal to the potential on its surface. Since the charge is positive, the potential will be positive.

Photocopiers use a process called xerography, which relies on electrostatics to attract charged toner particles to a photosensitive drum that has been exposed to an image.

An electroscope is a simple device used to detect the presence and sign of an electric charge by observing the repulsion of its thin metallic leaves.

First, find the equivalent capacitance for a parallel combination: C_eq = C1 + C2 = 10 μF + 20 μF = 30 μF. Then, find the total charge using Q_total = C_eq * V = (30 x 10⁻⁶ F) * (6 V) = 180 x 10⁻⁶ C, or 180 μC.

Relative permittivity (or dielectric constant) K = ε / ε₀, where ε is the permittivity of the medium and ε₀ is the permittivity of free space (a vacuum).

Charging by induction involves redistributing the charge on an object by bringing a charged object nearby, and then using a ground connection to remove some of that charge.

By definition, capacitance is C = Q/V. If C = 1 F and Q = 1 C, then V must be 1 V.

According to Newton's third law, the forces two objects exert on each other are always equal in magnitude and opposite in direction. This action-reaction pair applies to electrostatic forces as well.

Since the electric field inside is zero, no work is done moving a charge from the surface to any point inside. Therefore, the potential is constant throughout the conductor and equal to the potential at its surface.

In an inkjet printer, tiny ink droplets are given an electric charge and then passed through deflecting plates. The electric field between the plates directs the droplets precisely onto the paper.

In electrostatic equilibrium, the net electric field inside any conductor is zero. Any field would cause the free charges to move until the field is canceled out.

Use the electric field formula: E = k * |q| / r². Convert charge to Coulombs: q = 2 x 10⁻⁹ C. Then, E = (9 x 10⁹) * (2 x 10⁻⁹) / 3² = (9 x 10⁹) * (2 x 10⁻⁹) / 9 = 2 N/C.

An electric field has both magnitude (strength) and direction, making it a vector quantity. The others are scalar quantities.

Work done (W) is the charge (q) multiplied by the potential difference (ΔV). W = q(V_final - V_initial) = 4 C * (15 V - 10 V) = 4 C * 5 V = 20 J.

The formula for electric potential is V = kq/r. This shows that potential (V) is inversely proportional to the distance (r) from the point charge.

Positive potential energy implies a repulsive force. Work must be done on the system to bring two like charges (both positive or both negative) together. Option 2 is also correct, but typically only one is listed.

According to Coulomb's law, force is inversely proportional to the square of the distance (F ∝ 1/r²). If the distance is doubled (2r), the force becomes 1/(2r)² = 1/4 of the original force. 120 N / 4 = 30 N.

This unit can be derived from the Coulomb's law formula, F = (1/4πε₀)(q₁q₂/r²). Rearranging for ε₀ gives its units as C² / (N·m²).