At point P, the electric fields produced by the +1 nC charge on the left and the charge on the right add together. An electric field has both magnitude and direction.
Adjust conditions:
The sliders adjust the values
右10 cmに−1 nCを置く。Pの電場の大きさは、左だけのときの何倍か？
右も+1 nCにする。Pの電場の大きさは、左だけのときの何倍か？
The equations explain the phenomenon
1Coulomb's law gives the force.F=k |q₁ q₂|r²……
2The electric field is defined as the force divided by the test charge.E=Fq=k Qr²……
Steps 1–3 use the arrangement with +1 nC to the left of P and −1 nC to the right, which is the initial configuration in the diagram above.
3Determine the direction of the field from a negative chargeE₂=k |Q₂|r²(Toward Q₂)……
4The two electric fields add as vectors.The vector sum is:𝐄=𝐄₁+𝐄₂……
Further topics: extended charge distributions and electric fields in matter
5Further comparison: electrostatic force and gravityFelectricFgravity=1.2×10³⁶……
Electric flux through a small surface element = the electric field component perpendicular to the surface × the area, with outward taken as positive.The flux is positive when the electric field points outward, 0 when it is parallel to the surface, and negative when it points inward. For a closed surface, these contributions are summed over the entire surface.
6Calculate the electric flux through a spherical surfaceΦ=4π k Q……
7Gauss's law gives the field of a uniformly charged infinite plane.The plane extends infinitely.E=2π k σ……
8Two infinite plates face each other.Both plates extend infinitely.E=4π k σ=σε₀……
9A numerical calculation checks the field of finite plates.The field is evaluated near the center of wide plates.E≒4π k σ=σε₀……
10Electrons move within a metal.The metal reaches electrostatic equilibrium.Ein=0……
11A dielectric changes the electric field between the plates.Ein=E₀εr……
What this chapter has shown
The electric field at a point is the force on a small positive test charge placed there, divided by the test charge. It gives the force per 1 C of positive charge and exists even when no test charge is present. At the midpoint between equal + and − charges, the two fields point in the same direction and reinforce each other.
2.00 timesThe ratio to the field from the left charge alone
If the charge on the right is also +, the two fields at P point in opposite directions and cancel to give 0.
In everyday lifeA photocopier uses the electric field of a charged drum to attract toner powder, which is then transferred to paper.
Detailed summary
The electrostatic force has the same mathematical form as the gravitational force. The electric field expresses this force as the force per 1 C of positive electric charge at a given point. Because the electric field has a direction, the field produced by multiple charges is found by vector addition. At the midpoint between + and − charges, the 2 electric fields point in the same direction and reinforce each other; at the midpoint between equal + and + charges, they cancel. Electric flux and Gauss's law provide a common framework for explaining both the uniform electric field between plates and why the electric field inside a metal is 0.