Problem 43 - Master Resource Book in JEE Main Physics

Question

In the electric field shown in figure, the electric lines in the left have twice the separation as that between those on right. If the magnitude of the field at point \(A\) is \(40 \mathrm{NC}^{-1}\). The force experienced by a proton placed at point \(A\) is (a) \(6.4 \times 10^{-18} \mathrm{~N}\) (b) \(3.2 \times 10^{-15} \mathrm{~N}\) (c) \(5.0 \times 10^{-12} \mathrm{~N}\) (d) \(1.2 \times 10^{-18} \mathrm{~N}\)

Step-by-Step Solution

Answer

The correct answer is (a) \(6.4 \times 10^{-18} \mathrm{~N}\).

Step 1: Identify the Given Data

The problem provides the electric field magnitude at point \(A\) as \(40 \mathrm{NC}^{-1}\). We need to find the force experienced by a proton placed at this point.

Step 2: Understand the Formula for Electric Force

The force \(F\) on a charge \(q\) due to an electric field \(E\) can be calculated using the formula \(F = qE\). A proton has a charge \(q = 1.6 \times 10^{-19} \mathrm{C}\).

Step 3: Calculate the Electric Force

Substitute the known values into the formula: \(F = (1.6 \times 10^{-19} \mathrm{C}) \times (40 \mathrm{NC}^{-1})\). This simplifies to \(F = 6.4 \times 10^{-18} \mathrm{N}\).

Step 4: Select the Correct Answer

Compare the calculated force with the given options. The option that matches is (a) \(6.4 \times 10^{-18} \mathrm{~N}\).

Key Concepts

Electric Force

The electric force is a fundamental interaction that occurs between charged particles due to their electric fields. It is an essential concept in physics and plays a role in everything from the way atoms are held together to how electronic devices work. Electric force is the result of charges interacting and can be attractive or repulsive. Here, we focus on how this force acts on a charged particle within an electric field. If you have a charged object—like a proton—in an electric field, that electric field will exert a force on the charge. This electric force can be calculated using the formula

• \(F = qE\)

where \(F\) is the force in newtons (N), \(q\) is the charge in coulombs (C), and \(E\) is the electric field strength in newtons per coulomb (\(NC^{-1}\)). Understanding how electric fields interact with charges will help you explore more complex physics problems.

Proton Charge

Every proton carries a charge, and understanding this property is crucial when calculating forces in physics. The charge of a proton is one of the fundamental constants of nature. In any physics problem involving electric forces, knowing the charge of the proton is essential. To provide a clear perspective:

• A proton has a positive charge, denoted by \(q = 1.6 \times 10^{-19} \mathrm{C}\).
• The positive sign indicates that it is the opposite of the negative electron charge.

This charge is a small yet powerful quantity that we use as a basis for understanding interactions of matter on the atomic scale. The reactivity of atoms and molecules, and indeed much of chemistry and biology, hinges on these electrostatic interactions.

Calculation of Force

Calculating the force that a proton experiences in an electric field requires using well-known formulas. It's straightforward with the right information and formula. When a proton is placed in an electric field, the force it experiences can be calculated by multiplying the proton's charge by the magnitude of the electric field. Using the formula

• \(F = qE\)
• where \(q = 1.6 \times 10^{-19} \mathrm{C}\) (charge of a proton)
• and \(E = 40 \mathrm{NC}^{-1}\) (electric field at point \(A\))

we find the force by substituting these values. Substitution yields:

• \(F = (1.6 \times 10^{-19} \mathrm{C}) \times (40 \mathrm{NC}^{-1})\)
• \(F = 6.4 \times 10^{-18} \mathrm{N}\)

This result indicates the strength of the force acting on the proton at point \(A\), helping us determine how charged particles like protons behave within electric fields.