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Chapter 13: Problem 1969

Force between two identical bar magnets whose centers are I meter apart is \(4.8 \mathrm{~N}\), when their axes are in the same line. If separation is increased to \(2 r\), the force between them is reduced to (a) \(2.4 \mathrm{~N}\) (b) \(1.2 \mathrm{~N}\) (c) \(0.6 \mathrm{~N}\) (d) \(0.3 \mathrm{~N}\)

Short Answer

Expert verified
The short answer is: The force between the two identical bar magnets when their separation is increased to 2 meters is \(1.2 \mathrm{~N}\).

Step by step solution

01

Identify the formula for the force between two bar magnets

The force between two identical bar magnets can be represented as follows: \(F \propto \frac{m_1 m_2}{d^2}\) Where F is the force between the magnets, m_1 and m_2 are their magnetic moments, and d is the distance between them. Since the magnets are identical, we can simplify the formula as: \(F \propto \frac{m^2}{d^2}\) Here we can introduce a constant k to convert the proportionality to an equation: \(F = k\frac{m^2}{d^2}\)
02

Calculate the constant k using the initial conditions

We know that when the distance between the magnets is 1 meter, the force between them is 4.8 N. We will use this information to find the constant k: \(4.8 = k\frac{m^2}{(1)^2}\) Solving for k, \(k = 4.8m^2\)
03

Calculate the new force when the distance is increased to 2 meters

Now, we will use the equation to find the force when the distance between the magnets is increased to 2 meters: \(F_{new} = k\frac{m^2}{(2)^2}\) Substitute the value of k from Step 2: \(F_{new} = (4.8m^2)\frac{m^2}{(2)^2}\) Solve for \(F_{new}\): \(F_{new} = \frac{4.8m^4}{4}\) Simplify the expression: \(F_{new} = 1.2m^4\) In this situation, the new force F is proportional to \(1.2m^4\). Since the proportionality constant is the same as before, the new force can be represented as: \(F_{new} = 1.2(4.8)\) \(F_{new} = 1.2 \mathrm{~N}\)
04

Choose the correct answer

From the options provided: (a) 2.4 N (b) 1.2 N (c) 0.6 N (d) 0.3 N The correct answer is (b) 1.2 N, as calculated in the previous step.

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