Problem 4 - Arihant AIEEE Physics

Question

Five balls, numbered 1 to 5 are suspended using separate threads. Pairs \((1,2),(2,4),(4,1)\) show electrostatic attraction; while pairs \((2,3)\) and \((4,5)\) show repulsion therefore, ball 1 must be : (a) positively charged (b) negatively charged (c) neutral (d) made of metal

Step-by-Step Solution

Answer

Ball 1 is positively charged.

Step 1: Analyze Attraction and Repulsion

We know that like charges repel and opposite charges attract. Pairs (1,2), (2,4), and (4,1) show attraction, which means one must be positive and the other negative in each pair. Pairs (2,3) and (4,5) show repulsion, indicating that balls in these pairs have like charges.

Step 2: Determine Charges from Repulsion

Starting with pair (2,3) showing repulsion, balls 2 and 3 must have like charges. Similarly, in pair (4,5) showing repulsion, balls 4 and 5 must also have like charges.

Step 3: Assign Charges to Ball 2 and Ball 3

Since balls 2 and 3 repel each other, let's assume that ball 2 has a positive charge. Consequently, ball 3 must also have a positive charge.

Step 4: Assign Charge to Ball 4 Based on Attraction with Ball 2

Ball 2 has a positive charge, and since it attracts with ball 4, ball 4 must have a negative charge.

Step 5: Determine the Charge on Ball 1 Using Pair (4,1)

Ball 4 has a negative charge and attracts ball 1, hence ball 1 must have a positive charge to attract a negatively charged ball 4.

Key Concepts

Charge Interaction

In the world of electrostatics, understanding how charges interact is essential. Imagine charges as tiny magnets with invisible forces around them. These forces are the essence of charge interaction. The behavior of electrically charged particles is governed by two basic rules:

• Like charges repel
• Opposite charges attract

This means that if two objects both have a positive or a negative charge, they will push each other away. Conversely, if one object is positively charged and the other is negatively charged, they will pull towards each other.

Think of it as a seesaw of sorts. To maintain equilibrium, opposite charges balance each other. This underpins why some materials stick together, while others repel.

In our exercise with balls 1 to 5, understanding these interactions allows us to deduce the charge of each ball based on whether they attract or repel when placed in proximity.

Attraction and Repulsion

Attraction and repulsion are fundamental behaviors observed in electrostatics. They define the motion and positioning of charged bodies around us every day. But what causes these behavior patterns?

• Attraction occurs when opposite electrical charges come close to each other.
• Repulsion happens when similar charges try to occupy the same space.

For example, in the exercise, balls 1, 2, and 4 demonstrate attraction between different combinations, suggesting their charges differ. When two charges attract, it’s because the force between them is drawing them close together, despite their differences.

Conversely, observing repulsion in pairs like (2,3) and (4,5) tells us that each ball has a charge similar to their partner in the pair. The strength of these forces relies not only on the type of charge but on the distance separating them.

Thus, by harnessing knowledge of these basic principles, we can infer the unseeable forces at play and predict interactions.

Like Charges and Opposite Charges

The distinction between like charges and opposite charges is a pivotal concept in understanding electrostatic interactions. Like charges, which are either both positive or both negative, inherently repel each other.

On the other hand, opposite charges, where one is positive and the other negative, attract each other. This dual directional force helps explain the varied interactions observed amongst charged bodies.

• If two charges repel, then they must be alike.
• If two charges attract, they must be opposites.

In the example involving numbered balls, the combination of attractions and repulsions observed signifies these relationships. For example, when ball 2 is known to repel ball 3 and attract ball 4, we conclude they exhibit alike and opposite charges, respectively.

By applying these foundational concepts, we're able to decipher the enigmatic dance of electrons and deduce the invisible natures and quantities that define each charged object’s interaction.