Question

An oil drop is stationary within an electric field of \(490 \mathrm{~V} / \mathrm{m}\) that is set up between two parallel plates. If the volume of the oil drop is \(4 \times 10^{-19} \mathrm{~m}^3\), how many excess electrons does it carry? (Note: The fundamental unit of charge \(\mathrm{e}=1.6 \times 10^{-19} \mathrm{C}\).) 1\. \(\quad 1\) 2\. 4 3\. 10 4\. 40

Short answer

The short answer to the given question is: Option 2: 4 excess electrons

Step-by-step solution

Step 1:

Calculate mass of the oil drop Given: V = 4 * 10^-19 m³ Since density (ρ) of oil is 800 kg/m³, we can calculate mass (m) using the formula: m = V * ρ

Step 2:

Calculate gravitational force on the oil drop Given: g = 9.81 m/s² Calculate the gravitational force acting on the drop using the formula: F_g = m * g

Step 3:

Balance electric force with gravitational force Given: E = 490 V/m e = 1.6 * 10^-19 C Let n be the number of excess electrons on the oil drop, then the overall charge (q) will be: q = n * e The electric force acting on the oil drop is: F_e = q * E Since the oil drop is stationary, the electric force must be equal to the gravitational force: F_e = F_g n * e * E = m * g Now we will solve for n: n = (m * g) / (e * E)

Step 4:

Find the number of excess electrons and choose the correct answer Calculate the value of n using the derived equation and check which option matches the result. Option 1: 1 Option 2: 4 Option 3: 10 Option 4: 40

Key concepts

Official LSAT Exams

The Law School Admission Test (LSAT) plays a crucial role for aspiring lawyers aiming to enter prestigious law schools. The examination assesses key skills necessary for success in law school, including critical reading, analytical reasoning, and logical thinking.

Official LSAT exams are administered by the Law School Admission Council (LSAC) and are designed to measure candidates' readiness for law school. The Analytical Reasoning section, commonly referred to as 'Logic Games', is one where many test-takers seek to improve. It consists of puzzles that require the examinee to understand a set of rules and apply them to solve complex problems.

The significance of practicing with actual, official exams cannot be overstated. This provides an authentic gauge of the test format, question types, and timing pressures one will experience on test day. By consistently working through official LSAT problems, students become familiar with the test-makers' language and logic, which in turn helps build confidence and skill.

LSAT Problem Solving

Success in the Analytical Reasoning section of the LSAT entails a strategic approach to problem-solving. To tackle these problems effectively, understanding the process of elimination and the ability to identify inference patterns is crucial. Each game presented in this section comes with a distinct set of rules and requires a unique approach for arrangement, grouping, or matching elements based on those rules.

By dissecting these games into manageable parts—identifying the rules, setting up a base, and creating scenarios—candidates can systematically approach each question. Time management is critical; practice should focus on developing quick recognition of problem types and applying shortcuts to arrive at solutions more efficiently. LSAT problem-solving is less about complex mathematical calculations and more about logical reasoning and the effective application of given information, akin to solving a puzzle with a clear method to follow.

LSAT Preparation Strategies

Preparing for the LSAT is a marathon, not a sprint. It requires a consistent and well-thought-out strategy. Here are some key LSAT preparation strategies:

• Understand the Format: Familiarize yourself with the LSAT structure, timing, and question types.
• Study Schedule: Develop a study plan that allows for gradual improvement and includes regular practice tests.
• Practice with Purpose: Don't just practice for the sake of practice. Analyze your mistakes and understand why the correct answers are correct.
• Master Logical Reasoning: Focus on improving your logical reasoning skills, as they are vital across all sections of the test.
• Timed Practice: Simulate testing conditions by taking full-length, timed practice exams.
• Seek Feedback: Review explanations for both correct and incorrect answers. If possible, work with a tutor or study group to gain new perspectives.
• Stay Healthy: Maintain a balanced diet, exercise regularly, and ensure adequate sleep to keep your mind sharp.

Implement these strategies consistently, and you'll be on the path to maximizing your LSAT score.