**Problem Description:**Location A is 1.70 m to the right of a point charge \( q \). Location B lies on the same line and is 5.40 m to the right of the charge. The potential difference \( V_B - V_A = -57.0 \, \text{V} \). What is the magnitude and sign of the charge?**Diagram Explanation:**The diagram shows a horizontal line with a point labeled \( q \) (representing the charge) on the left. To the right of this point, there are two more labeled points: \( A \) and \( B \).- The distance from the charge \( q \) to location \( A \) is labeled \( r_A = 1.70 \, \text{m} \).- The distance from the charge \( q \) to location \( B \) is labeled \( r_B = 5.40 \, \text{m} \).**Input Fields:**- There is a field labeled "Number" for entering the calculated value.- A dropdown menu labeled "Units" allows the selection of units for the charge.This problem involves calculating the magnitude and sign of a point charge based on the given potential difference and distances.

Given data: Distance between the charge and point A, rA=1.70 m Distance between the charge and point B, rB=5.40 m The potential difference, VB-VA=57 V Our question is to find the magnitude and sign of the charge.Solution: The electric potential (V) at a point r from charge q is given by the formula, V=kqr (1) k - Columb constant = 9×109 N.m2.C-2 q - Charge r - Distance from the charge So, the electric potential at point A is, VA=kqrA (2) Similarly, the electric potential at point B is, VB=kqrB (3) Now, it is given that, VB-VA=57 V (4) Substitute equation (2) and (3) in (4) kqrB-kqrA=57 V⇒kq1rB-1rA=57 V⇒q=57 Vk1rB-1rA⇒q=57 VkrA-rBrArB⇒q=57 V×rArBk(rA-rB) (5) Now, substitute the values in equation (5) ⇒q=57 V×1.70 m×5.40 m9×109 Nm2C-2×1.70 m-5.40 m⇒q=523.26-3.33×1010 C⇒q=-1.57×10-8 C⇒q=-15.7×10-9 C⇒q=-15.7 nC So, The magnitude of charge =15.7 nC Sign of the charge = Negative

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Location A is 1.70 m to the right of a point charge q. Location B lies on the same line and is 5.40 m to the right of the charge. The potential difference V₁-V₁-57.0 V. What is the magnitude and sign of the charge? A Number Units

Location A is 1.70 m to the right of a point charge q. Location B lies on the same line and is 5.40 m to the right of the charge. The potential difference V₁-V₁-57.0 V. What is the magnitude and sign of the charge? A Number Units

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

**Problem Description:**

Location A is 1.70 m to the right of a point charge \( q \). Location B lies on the same line and is 5.40 m to the right of the charge. The potential difference \( V_B - V_A = -57.0 \, \text{V} \). What is the magnitude and sign of the charge?

**Diagram Explanation:**

The diagram shows a horizontal line with a point labeled \( q \) (representing the charge) on the left. To the right of this point, there are two more labeled points: \( A \) and \( B \).

- The distance from the charge \( q \) to location \( A \) is labeled \( r_A = 1.70 \, \text{m} \).
- The distance from the charge \( q \) to location \( B \) is labeled \( r_B = 5.40 \, \text{m} \).

**Input Fields:**

- There is a field labeled "Number" for entering the calculated value.
- A dropdown menu labeled "Units" allows the selection of units for the charge.

This problem involves calculating the magnitude and sign of a point charge based on the given potential difference and distances.

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