Two point charges, 3.4 μC and -2.0 μC, are placed 8.0 cm apart on the x axis. At what points along the x axis are
(a) the electric field zero and
(b) the potential zero? Let V = 0 at r = ∞.

검증된 단계별 안내

Convert the given quantities into standard SI units: the charges are q₁ = 3.4 × 10⁻⁶ C and q₂ = -2.0 × 10⁻⁶ C, and the distance between them is d = 0.08 m.

To find where the electric field is zero (part a), recall that the electric field due to a point charge is given by E = (1 / (4πε₀)) * (q / r²). The net electric field will be zero at a point where the magnitudes of the electric fields due to both charges are equal and opposite. Set up the equation: (q₁ / r₁²) = (|q₂| / r₂²), where r₁ is the distance from q₁ to the point, and r₂ is the distance from q₂ to the point. Use the relationship r₁ + r₂ = d to express r₂ in terms of r₁ and solve for r₁.

To find where the potential is zero (part b), recall that the electric potential due to a point charge is V = (1 / (4πε₀)) * (q / r). The net potential will be zero at a point where the algebraic sum of the potentials due to both charges is zero. Set up the equation: (q₁ / r₁) + (q₂ / r₂) = 0. Again, use the relationship r₁ + r₂ = d to express r₂ in terms of r₁ and solve for r₁.

For both parts, solve the resulting equations algebraically to find the distances r₁ and r₂. Note that for part (a), the point where the electric field is zero must lie between the charges if they are of opposite signs, while for part (b), the point where the potential is zero can lie either between the charges or outside the region between them.

Verify the solutions by substituting the calculated distances back into the respective equations for electric field and potential to ensure that the conditions (E = 0 and V = 0) are satisfied.

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10m

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Electric Field

The electric field is a vector field that represents the force exerted by an electric charge on other charges in its vicinity. It is defined as the force per unit charge and is directed away from positive charges and towards negative charges. The electric field can be calculated using Coulomb's law, which describes the interaction between point charges.

Electric Potential

Electric potential, or voltage, is a scalar quantity that represents the potential energy per unit charge at a point in an electric field. It indicates how much work would be done to move a charge from a reference point (usually at infinity) to a specific point in the field. The potential is zero at infinity, and it can be calculated by integrating the electric field along a path.

Superposition Principle

The superposition principle states that the total electric field or potential at a point due to multiple charges is the vector sum of the fields or potentials due to each charge individually. This principle allows us to analyze complex charge configurations by considering the contributions from each charge separately, making it essential for solving problems involving multiple point charges.