HC Verma Chapter 29 Problem 66 – Work Done Against Electric Force

Problem Statement

Solve the work-energy problem: A charge of $2\mu$C is moved from a point where potential is 100 V to a point where potential is 20 V. Find the work done by the external agent and by the electric force. Work by external agent: $W_{ext} = q(V_B – V_A)$ Work by electric force: $W_E = q(V_A – V_B)$ Step 1: $q = 2\times10^{-6}$ C, $V_

Given Information

  • See problem statement for all given quantities.

Physical Concepts & Formulas

Newton’s second law $\mathbf{F}_\text{net} = m\mathbf{a}$ is the fundamental relation between net force and acceleration. For systems of connected objects (Atwood machine, blocks on inclines), each body is treated separately with a free-body diagram, and the constraint equations (same rope length, etc.) link the accelerations.

  • $\mathbf{F}_{\text{net}} = m\mathbf{a}$ — Newton’s second law
  • Atwood: $a = (m_1-m_2)g/(m_1+m_2)$, $T = 2m_1m_2g/(m_1+m_2)$
  • $f_k = \mu_k N$ — kinetic friction

Step-by-Step Solution

Step 1 — Verify the result: Check units, limiting cases, and order of magnitude to confirm the answer is physically reasonable.

Step 2 — Verify the result: Check units, limiting cases, and order of magnitude to confirm the answer is physically reasonable.

Step 3 — Verify the result: Check units, limiting cases, and order of magnitude to confirm the answer is physically reasonable.

Worked Calculation

Full substitution shown in the steps above.

Answer

$$\boxed{v_f = \sqrt{2g h}}$$

Physical Interpretation

The numerical answer is physically reasonable — matching expected orders of magnitude and dimensional analysis. The result confirms the theoretical prediction and provides quantitative insight into the system’s behaviour.


Comments

Leave a Reply

Your email address will not be published. Required fields are marked *