Two charges q1 and q2 are placed 30 cm apart, as shown in the figure. A third charge q3 is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is\(\bigg(\frac{q_3}{4\pi\in_0}\bigg)k\),where k is:
Two charges q1 and q2 are placed 30 cm apart, as shown in the figure. A third charge q3 is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is\(\bigg(\frac{q_3}{4\pi\in_0}\bigg)k\),where k is:
8q2
8q1
4q2
4q1
The Correct Option is A
Solution and Explanation
u1 =14\(\pi\in_0\)[q1q2 30×10−2+q1q2 40×10-2+q2q3 50×10-2 ]
u2 =14\(\pi\in_0\)[q1q2 30×10−2+q1q3 40×10-2+q2q310×10-2 ]
Δu= u2−u1=q2q34\(\pi\in_0\)×102[110−150]
=q2q34\(\pi\in_0\)×450×100
=q34\(\pi\in_0\)(8q2)
∴k=8q2
Therefore, the correct option is (A): 8q2
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Concepts Used:
Potential Energy
The energy retained by an object as a result of its stationery position is known as potential energy. The intrinsic energy of the body to its static position is known as potential energy.
The joule, abbreviated J, is the SI unit of potential energy. William Rankine, a Scottish engineer, and physicist coined the word "potential energy" in the nineteenth century. Elastic potential energy and gravitational potential energy are the two types of potential energy.
Potential Energy Formula:
The formula for gravitational potential energy is
PE = mgh
Where,
- m is the mass in kilograms
- g is the acceleration due to gravity
- h is the height in meters
Types of Potential Energy:
Potential energy is one of the two main forms of energy, along with kinetic energy. There are two main types of potential energy and they are:
- Gravitational Potential Energy
- Elastic Potential Energy