Problem 53 - Master Resource Book in JEE Main Physics

Question

Two plates are \(1 \mathrm{~cm}\) apart, and potential difference between them is 10 volt. The electric field between the plates is (a) \(10 \mathrm{~N} / \mathrm{C}\) (b) \(500 \mathrm{~N} / \mathrm{C}\) (c) \(10^{3} \mathrm{~N} / \mathrm{C}\) (d) \(250 \mathrm{~N} / \mathrm{C}\)

Step-by-Step Solution

Answer

The electric field is (c) \( 10^{3} \text{ N/C} \).

Step 1: Understand the formula for Electric Field

The electric field (E) between two plates is given by the formula \( E = \frac{V}{d} \), where \( V \) is the potential difference and \( d \) is the distance between the plates. In this context, \( V = 10 \text{ volts} \) and \( d = 1 \text{ cm} \).

Step 2: Convert Distance to Meters

Since the standard units for electric field calculation require distance in meters, first convert the distance: \( 1 \text{ cm} = 0.01 \text{ meters} \).

Step 3: Substitute Values into the Formula

Using the values \( V = 10 \text{ volts} \) and \( d = 0.01 \text{ meters}\), substitute them into the formula: \( E = \frac{10}{0.01} \).

Step 4: Perform the Calculation

Calculate the electric field: \( E = \frac{10}{0.01} = 1000 \text{ N/C} \).

Step 5: Identify the Correct Option

Compare the calculated electric field \( 1000 \text{ N/C} \) with the given options to find the correct answer. The correct option is (c) \( 10^{3} \text{ N/C} \).

Key Concepts

Potential Difference

The potential difference is a fundamental concept in electromagnetism. It refers to the voltage or electrical potential energy per unit charge between two points. In simpler terms, potential difference is the measure of how much work is needed to move a charge from one point to another. It is expressed in volts (V).

In the context of the problem, the potential difference between the two plates is given as 10 volts. This value indicates the energy needed to move a unit charge between these plates. The potential difference drives the electric field, impacting the force experienced by charges within it.

Distance Conversion

Distance conversion is crucial when dealing with scientific calculations, particularly in electromagnetism. Measurements need to be in standard units to ensure accuracy and consistency.

When calculating the electric field, the distance between the plates (originally given in centimeters) must be converted to meters. The SI unit of distance is the meter. For conversions:

• 1 centimeter is equal to 0.01 meters.

Thus, the conversion ensures we maintain standard measurement units, which gives us a distance of 0.01 meters in our calculations.

Unit Conversion

Unit conversion plays a vital role in the correct application of physics formulas. It ensures consistency in measurements, especially when dealing with different metrics.

In this scenario, we are transforming the unit from centimeters to meters for distance because the electric field formula uses meters as the standard unit. Always remember to:

• Convert units before substituting them into formulas.
• Check if units align with the standard SI units often used in formulas.

Doing so helps avoid calculation errors and ensures precise results.

Formula Application

Applying the correct formula accurately is essential for solving electromagnetism problems. The electric field (E) between two plates can be calculated using the formula:
\[ E = \frac{V}{d} \]
Here,

• \( V \) represents the potential difference, measured in volts.
• \( d \) represents the distance, measured in meters.

Substituting the given values, with

• \( V = 10 \text{ volts} \)
• and \( d = 0.01 \text{ meters} \),

we get:
\[ E = \frac{10}{0.01} = 1000 \text{ N/C} \]
This application helps find out how the potential difference and the distance can determine the electric field. Make sure to plug values into the equation properly for an accurate solution.