Câu 14: Công của lực điện trường dịch chuyển một điện tích 5.10-6 C ngược chiều một đường sứctrong một điện trường đều 1000 V/m trên quãng đường dài 0,5 m là

Break Down the Problem

1. Identify the given values:

   • Electric charge, $q = 5 \times 10^{-6} \, C$
   • Electric field strength, $E = 1000 \, V/m$
   • Distance moved against the electric field, $d = 0.5 \, m$

2. Understand the formula for work done by the electric field: $W = q \cdot E \cdot d \cdot \cos(\theta)$ Where $\theta$ is the angle between the electric field direction and the displacement. In this case, since the charge moves against the field:

   • $\theta = 180^\circ$ leading to $\cos(180^\circ) = -1$

Relevant Concepts

• Work done $W$ can be calculated using the formula: $W = q \cdot E \cdot d \cdot \cos(\theta)$

Analysis and Detail

1. Substitute the values into the equation: $W = (5 \times 10^{-6} \, C) \cdot (1000 \, \frac{V}{m}) \cdot (0.5 \, m) \cdot \cos(180^\circ)$
2. Calculate the cosine value: $\cos(180^\circ) = -1$
3. Therefore, $W = (5 \times 10^{-6}) \cdot (1000) \cdot (0.5) \cdot (-1)$ $W = -5 \times 10^{-6} \cdot 1000 \cdot 0.5$

Calculation Steps

1. Calculate $1000 \times 0.5$: $1000 \times 0.5 = 500$
2. Now calculate: $W = -5 \times 10^{-6} \cdot 500 = -2.5 \times 10^{-3} \, J$

Verify and Summarize

• The work done is negative because the electric field does work against the direction of the displacement. This result means energy is required to move the charge against the electric field.

Final Answer

The work done by the electric field in moving the charge is: $W = -2.5 \times 10^{-3} \, J$