Electric Field Physics Example 4

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Example 4

hard
Two point charges are placed on the x-axis: q1=+3×10−6 Cq_1 = +3 \times 10^{-6} \text{ C} at x=0x = 0 and q2=+3×10−6 Cq_2 = +3 \times 10^{-6} \text{ C} at x=0.4 mx = 0.4 \text{ m}. Find the electric field at the midpoint (x=0.2 mx = 0.2 \text{ m}). Use k=9×109k = 9 \times 10^9.

Solution

  1. 1
    At the midpoint, r=0.2 mr = 0.2 \text{ m} from each charge.
  2. 2
    E1=kq1r2=9×109×3×10−60.04=675,000 N/CE_1 = k\frac{q_1}{r^2} = 9 \times 10^9 \times \frac{3 \times 10^{-6}}{0.04} = 675{,}000 \text{ N/C} pointing right (away from q1q_1).
  3. 3
    E2=kq2r2=675,000 N/CE_2 = k\frac{q_2}{r^2} = 675{,}000 \text{ N/C} pointing left (away from q2q_2).
  4. 4
    The two fields are equal in magnitude but opposite in direction: Enet=675,000−675,000=0E_{\text{net}} = 675{,}000 - 675{,}000 = 0.

Answer

Enet=0 N/C at the midpointE_{\text{net}} = 0 \text{ N/C at the midpoint}
By symmetry, two identical charges produce equal and opposite electric fields at their midpoint, resulting in zero net field. This only works at the midpoint for identical charges — any other point would have a non-zero field.

About Electric Field

A region around a charged object where other charges experience a force. Measured in newtons per coulomb (N/C) or volts per meter (V/m).

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What is the electric field [formula] from a point charge of [formula]? Use [formula].

Example 2 medium

A charge of [formula] is placed in an electric field of [formula]. What force does it experience?

Example 3 hard

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