2. Three point charges are fixed in place at the corners of a trapezoid as shown. The upper side has length 3.0 cm, the base has length 5.0 cm and the height is 3.0 cm. q, =+ 10.0 nC, 3 cm =- 5.0 nC, and q, =+ 5. 0 nC. 92 a. Find the electric field at point P, the lower left corner of the trapezoid. b. Find the electric potential at point P taking the potential at infinity to be zero. 3 cm| -27 = 1.67 x 10 "kg) c. Suppose a proton (m is placed at point P and is released from rest. What will its speed be when it is very far from the arrangement of charges? P 1 cm 3 cm 1 cm

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PLEASE USE VECTOR ADDITION!

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**Problem 2:**

Three point charges are fixed in place at the corners of a trapezoid as shown. The upper side has a length of 3.0 cm, the base has a length of 5.0 cm, and the height is 3.0 cm. The charges are as follows: 

- \( q_1 = +10.0 \, \text{nC} \)
- \( q_2 = -5.0 \, \text{nC} \)
- \( q_3 = +5.0 \, \text{nC} \)

**a.** Find the electric field at point \( P \), the lower left corner of the trapezoid.

**b.** Find the electric potential at point \( P \) taking the potential at infinity to be zero.

**c.** Suppose a proton \(( m = 1.67 \times 10^{-27} \, \text{kg} )\) is placed at point \( P \) and is released from rest. What will its speed be when it is very far from the arrangement of charges?

**Diagram Description:**

The diagram on the right illustrates a trapezoid with charges at three corners:

- Charge \( q_1 \) is at the top left corner.
- Charge \( q_2 \) is at the top right corner.
- Charge \( q_3 \) is at the bottom right corner.
- Point \( P \) is at the bottom left corner, 1 cm from \( q_1 \).

The trapezoid has vertical dashed lines representing the height, marked as 3 cm. The top side of the trapezoid is 3 cm long. Additional horizontal guidelines indicate dimensions of 3 cm on either side from point \( P \) to points directly below \( q_1 \) and \( q_2 \).
Transcribed Image Text:**Problem 2:** Three point charges are fixed in place at the corners of a trapezoid as shown. The upper side has a length of 3.0 cm, the base has a length of 5.0 cm, and the height is 3.0 cm. The charges are as follows: - \( q_1 = +10.0 \, \text{nC} \) - \( q_2 = -5.0 \, \text{nC} \) - \( q_3 = +5.0 \, \text{nC} \) **a.** Find the electric field at point \( P \), the lower left corner of the trapezoid. **b.** Find the electric potential at point \( P \) taking the potential at infinity to be zero. **c.** Suppose a proton \(( m = 1.67 \times 10^{-27} \, \text{kg} )\) is placed at point \( P \) and is released from rest. What will its speed be when it is very far from the arrangement of charges? **Diagram Description:** The diagram on the right illustrates a trapezoid with charges at three corners: - Charge \( q_1 \) is at the top left corner. - Charge \( q_2 \) is at the top right corner. - Charge \( q_3 \) is at the bottom right corner. - Point \( P \) is at the bottom left corner, 1 cm from \( q_1 \). The trapezoid has vertical dashed lines representing the height, marked as 3 cm. The top side of the trapezoid is 3 cm long. Additional horizontal guidelines indicate dimensions of 3 cm on either side from point \( P \) to points directly below \( q_1 \) and \( q_2 \).
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