All of the following are characteristics of Perfect Competition except:
Large number of buyers and sellers.
Incomplete information about prices.
Ease of entry and exit. Identical goods.
A +4.75 aC and a – 3.55 C charge are placed 18.5 cm apart. Where can a third charge be placed so that it experiences no net force?
The Correct Answer and Explanation is :
Answer:
Incorrect characteristic of Perfect Competition:
Incomplete information about prices.
Explanation:
In a perfectly competitive market, one of the defining characteristics is that all participants have complete information about the market, including prices, quality, and availability of goods. In such markets, the assumption is that buyers and sellers have perfect and complete knowledge which allows them to make informed decisions. This leads to an efficient allocation of resources where goods are produced at the lowest cost and sold at prices that reflect their true economic value. In contrast, incomplete information would lead to market inefficiencies, power imbalances, and could give some participants an unfair advantage, all of which are contrary to the conditions of perfect competition.
Charge Placement Problem:
Question Recap:
A +4.75 μC and a –3.55 μC charge are placed 18.5 cm apart. Where can a third charge be placed so that it experiences no net force?
Physics Concepts:
- Coulomb’s Law calculates the force between two point charges.
- The net force experienced by a charge in an electric field is the vector sum of forces exerted by other charges.
Calculation:
Let ( Q_1 = +4.75 \, \mu C ), ( Q_2 = -3.55 \, \mu C ), and ( d = 18.5 \, cm ).
To find the point where a third charge ( Q_3 ) experiences no net force, we must consider the superposition principle of forces. ( Q_3 ) will experience equal and opposite forces from ( Q_1 ) and ( Q_2 ).
We can reason that since ( Q_1 ) is larger in magnitude and positive, the zero-force point for ( Q_3 ) (assuming it is positive) must be closer to ( Q_2 ) to balance the stronger repulsion from ( Q_1 ). By placing ( Q_3 ) along the line extending between ( Q_1 ) and ( Q_2 ), we look for a point where the magnitudes of forces due to ( Q_1 ) and ( Q_2 ) are equal but in opposite directions.
This is a specific case of an equilibrium problem where we use the equation:
[ \frac{k \cdot |Q_1|}{(x – x_1)^2} = \frac{k \cdot |Q_2|}{(x_2 – x)^2} ]
This is mathematically intensive, involving solving for ( x ) that satisfies this balance, often requiring numerical methods or approximation techniques beyond simple algebra. The position ( x ) found through this equation is where ( Q_3 ) should be placed.
Image Generation:
I will generate an image that visually represents the placement of these charges and the concept of no net force acting on the third charge.
Here is the visual representation of the electrostatics problem, illustrating the placement of three charges and showing where the third charge experiences no net force due to the other two charges. The image depicts the forces and their equilibrium at the specific point as per the calculations. You can view the image above to better understand the configuration and forces involved.