Problem 57 - Master Resource Book in JEE Main Physics

Question

A glass rod rubbed with silk is used to charged a gold leaf electroscope and the leaves are observed to diverse. The electroscope thin, charged is exposed to X-rays for short period. Then, (a) the leaves will diverge further (b) the leaves will melt (c) the leaves will not be affected (d) None of the above

Step-by-Step Solution

Answer

(d) None of the above.

Step 1: Understand the Problem

When a glass rod is rubbed with silk, it becomes positively charged. If this rod is used to charge a gold leaf electroscope, the leaves will diverge because they are charged with the same type of charge and like charges repel each other.

Step 2: Understand the Effect of X-Rays

X-rays are capable of ionizing air and other materials by removing electrons, which creates free electrons that neutralize positive charges. When X-rays are applied to a charged electroscope, they will cause the electroscope to lose its positive charge by providing electrons to neutralize it.

Step 3: Predict the Effect of X-Rays on the Electroscope

Because the X-rays neutralize the positive charge on the electroscope, the leaflets are no longer repelled by each other, causing them to fall back to their neutral position or nearly so. Thus, the leaves of the electroscope will converge rather than diverge further.

Step 4: Review Given Options

The options are (a) the leaves will diverge further, (b) the leaves will melt, (c) the leaves will not be affected, (d) None of the above. Given the deduction that the leaves will converge, option (d) is correct because the leaves will actually converge, not diverge or remain unaffected.

Key Concepts

X-rays effect

X-rays are a form of electromagnetic radiation, similar to visible light but with much higher energy. They have the ability to pass through matter and affect it on a molecular level. X-rays can ionize atoms by liberating electrons, which plays a crucial role in various scientific and medical applications. This ionization process is where X-rays interact with the matter they penetrate, particularly the air surrounding an object like a charged electroscope.

When X-rays pass through the air, they can knock out tightly held electrons from gas molecules, creating free electrons and positively charged ions. This creates an environment rich in electrons that can neutralize any positive charges in objects like an electroscope. Thus, in the context of this electroscope problem, the presence of X-rays allows for the neutralization of the positive charges acquired initially by the electroscope, causing the leaves to no longer repel each other and begin to converge.

Charge neutralization

Charge neutralization is a process where an object's net charge is brought closer to zero by either gaining or losing electrons. In electrostatics, an object becomes charged by having an imbalance of protons and electrons. By introducing additional charges or removing some, the balance gets restored to neutral or zero net charge.

In our case with the electroscope, initially charged with a glass rod resulting in positive charge due to deficit of electrons, the ionizing effect of X-rays can bring about neutralization. The X-rays free electrons in the surrounding air, which then get attracted to the positively charged electroscope. This influx of electrons effectively neutralizes the positive charge, causing the leaves that were spread apart due to repulsion of like charges to fall back towards each other.

• Excess positive charge: Electrons are attracted to reduce the charges.
• Excess negative charge: Electrons are repelled to restore neutrality.

In this manner, charge neutralization makes static electric systems like the electroscope stable and balanced again.

Electrostatics

Electrostatics is the study of electric charges at rest. It involves understanding the forces, fields, and potentials produced by static electric charges, both on conductors and insulators. It is a crucial principle in physics, underlying many electric phenomena and applications.

The basic premise involves how charges interact with one another. Like charges repel, whereas opposite charges attract. This is the reason why when a gold leaf electroscope is charged, its leaves diverge or spread apart, as they hold like charges. The electric force between the leaves, which are charged with the same sign, causes them to repel each other, leading to the divergence observed.

• Charge interaction: Like charges repel; opposite charges attract.
• Charging methods: Objects can be charged through friction, conduction, or induction.

The study of electrostatics allows us to predict and explain such behaviors in various situations, ultimately bridging toward understanding electrical phenomena in both theoretical and practical realms.