Problem 107 - Master Resource Book in JEE Main Physics

Question

Electric potential and electric potential energy both are (a) scalars (b) vectors (c) both (a) and (b) (d) neither (a) nor (b)

Step-by-Step Solution

Answer

(a) scalars

Step 1: Understand the Definitions

Electric potential is the amount of electric potential energy per unit charge at a point in a field. It is a scalar quantity, meaning it has only magnitude and no direction. Similarly, electric potential energy is the energy a charge has due to its position in an electric field. It is also a scalar quantity.

Step 2: Identify Key Characteristics

Identify that both electric potential and electric potential energy do not have directions; they only have magnitudes. This is a fundamental characteristic of scalar quantities.

Step 3: Analyze Options

Given that both are scalar quantities, we need to select the option that represents this correctly which is (a) scalars.

Step 4: Conclusion

Since both electric potential and electric potential energy are scalars, they do not fulfill the characteristics of vectors, which have both magnitude and direction. Thus, the correct answer is option (a).

Key Concepts

Electric Potential Energy

Electric potential energy represents the energy that a charge possesses because of its position in an electric field. Just like gravitational potential energy, which depends on an object's height relative to the Earth, electric potential energy depends on a charge's position within an electric field. The higher the charge and the stronger the electric field, the greater the electric potential energy. This energy is crucial when calculating the work done by or against an electric field when moving a charge from one point to another. Key points to remember:

• Electric potential energy depends on the amount of charge and the electric field.
• It is a scalar quantity, meaning it has only magnitude.
• This energy can be transformed into kinetic energy as charges move.

Scalar Quantity

A scalar quantity is one that is fully described by a numerical value alone. It does not have a direction component. This is different from vectors, which require both magnitude and direction for their description. Examples of scalar quantities in physics include:

• Electric potential
• Electric potential energy
• Temperature
• Mass
• Length

In the context of electric potential and electric potential energy, the scalar nature simplifies calculations, as you only need to handle magnitudes without dealing with directional vectors. Remember:

• Scalars are simple and easy to work with.
• Having only magnitude means less complexity in calculations.

Electric Field

An electric field is a region around a charged object where a force would be experienced by other charges. It extends outward, affecting any charged particles within its reach. The strength of an electric field at any point is determined by the amount of charge creating the field and the distance from the charge. Electric fields can be represented by field lines, which show the direction of the force that would act on a positive test charge. These fields are vector quantities, possessing both magnitude and direction. Important characteristics:

• The lines start on positive charges and end on negative charges.
• The density of these lines indicates the strength of the field.
• In a uniform electric field, the field strength is constant across the area.

Charge

Charge is a fundamental property of matter that causes it to experience a force when placed in an electric or magnetic field. There are two types of electric charges: positive and negative. Opposite charges attract each other, while like charges repel. The interaction between charges is responsible for many electrical phenomena. Essential attributes of charge:

• Measurable in coulombs (C).
• Intrinsic to particles like electrons (negative charge) and protons (positive charge).
• A unit charge, such as an electron or proton, has a known, fixed quantity of charge.
• Charges produce electric fields and influence electric potential energy.