Electric Potential and Energy in Electrostatics Quiz Quiz

Explore the fundamentals of electric potential and energy in electrostatics with these challenging questions. This quiz covers key concepts such as potential difference, equipotential surfaces, the work-energy relationship, and charge distributions, making it ideal for those seeking to strengthen their understanding of electrostatic phenomena.

1. Basic Electric Potential Calculation

   A point charge of +3 microcoulombs is located at the origin. What is the electric potential at a point 2 meters away from the charge in free space (take k = 9 × 10^9 N·m²/C²)?

   1. 27000 V
   2. 5400 V
   3. 9000 V
   4. 13500 V

   Explanation: The electric potential V at a distance r from a point charge Q is given by V = kQ/r. Substituting values, V = 9 × 10^9 × 3 × 10^-6 / 2 = 13500 V. The other options result from calculation errors: 5400 V involves multiplying instead of dividing, 27000 V ignores the division by distance, and 9000 V uses an incorrect charge value. It's important to use the proper formula and units.

2. Equipotential Surfaces Understanding

   Which statement best describes an equipotential surface near a positive point charge?

   1. The potential is zero everywhere on the surface.
   2. Work is required to move a charge along the surface.
   3. The electric field is always parallel to the surface.
   4. All points on the surface have the same electric potential.

   Explanation: Equipotential surfaces are defined so that every point on them has the same electric potential, making this the correct answer. The electric field is actually perpendicular, not parallel, to such surfaces, making the second option incorrect. Since potential is constant, no work is required to move a charge along the surface, so the third option is wrong. The fourth option is false since the potential is not necessarily zero on equipotentials near a charge.

3. Work Required Against Electric Field

   How much work is required to move a 2 microcoulomb test charge from a point with a potential of 500 V to one with 200 V?

   1. -0.0003 J
   2. 0.0003 J
   3. 0.0006 J
   4. -0.0006 J

   Explanation: Work done (W) is given by q × ΔV = 2 × 10^-6 × (200 - 500) = 2 × 10^-6 × (-300) = -0.0006 J. The negative sign means the work is done by the field, not against it. Selecting 0.0006 J ignores the sign. 0.0003 J and -0.0003 J stem from an incorrect potential difference of 100 V, not 300 V, leading to wrong values.

4. Potential Energy in a System

   If two identical charges of +4 microcoulombs are placed 10 cm apart in vacuum, what happens to the potential energy if the distance doubles?

   1. Potential energy doubles.
   2. Potential energy becomes half its original value.
   3. Potential energy becomes four times less.
   4. Potential energy remains unchanged.

   Explanation: Electrostatic potential energy between two charges is inversely proportional to their separation. If the distance doubles, potential energy becomes half. Doubling potential energy is incorrect, as that would require halving distance. The potential energy does change, so 'remains unchanged' is wrong. 'Four times less' is incorrect, as this would happen only if the distance was increased fourfold.

5. Electric Potential inside a Conductor

   What is the electric potential at any point inside a charged solid conductor at electrostatic equilibrium?

   1. It is constant throughout the conductor.
   2. It is zero only at the center.
   3. It varies depending on location inside.
   4. It is highest at the surface and zero inside.

   Explanation: At electrostatic equilibrium, the electric potential is uniform everywhere inside a conductor because charges distribute themselves to neutralize any internal fields. 'Zero only at the center' and 'varies depending on location inside' are incorrect as both contradict the property of equilibrium. 'Highest at the surface and zero inside' is wrong; the constant value applies to the entire volume including the surface.