Which one of the following is a scalar quantity (has magnitude only but no direction associated with it)?

Introduction / Context:
In physics, physical quantities are classified as scalars or vectors. Scalars have only magnitude, while vectors have both magnitude and direction. Correctly identifying whether a quantity is scalar or vector is important for solving problems in mechanics, electromagnetism and other branches of physics. This question asks you to pick the only scalar quantity from a list that includes both scalar and vector physical quantities.

Given Data / Assumptions:

• The options are power, electric field, magnetic moment and average velocity.
• Scalars are fully described by a numerical value and unit.
• Vectors need both magnitude and a specific direction in space.
• We assume standard physics definitions for these quantities.

Concept / Approach:
Power is defined as the rate of doing work or the rate of energy transfer, typically written as P = dW/dt. Work and energy are scalar quantities, and their time rate is also a scalar. Electric field is a vector field; at every point in space, it has both magnitude and direction, describing the force per unit positive charge. Magnetic moment is also a vector quantity associated with the orientation of current loops or magnets. Average velocity is defined as total displacement divided by total time and displacement is a vector, so average velocity is also a vector.

Step-by-Step Solution:
Step 1: Recall that scalars have magnitude only, while vectors have both magnitude and direction.Step 2: Consider power: it measures how fast work is done and is given by P = W/t or dW/dt, which does not include a direction component; thus it is a scalar.Step 3: Consider electric field: by definition, it is the force per unit charge and has a direction of the force, so it is a vector.Step 4: Consider magnetic moment: it describes the strength and orientation of a magnet or current loop and has a definite direction, so it is a vector.Step 5: Consider average velocity: it is displacement divided by time and displacement has direction, making average velocity a vector.Step 6: Conclude that among the four, only power is a scalar quantity.

Verification / Alternative check:
Mathematically, vector quantities obey vector addition rules and can be represented with arrows. Electric fields and velocities are often drawn as arrows on diagrams. Magnetic moment is also shown with arrows to indicate orientation. Power, however, is never represented with an arrow; it is just a numerical value such as 60 W or 1000 W. Furthermore, power does not need a direction to be fully described, which confirms its scalar nature.

Why Other Options Are Wrong:
Electric field is vectorial because it tells you not only how strong the field is but also the direction in which a positive test charge would be pushed. Magnetic moment involves orientation and is treated as a vector in torque and energy expressions. Average velocity gives both speed and the direction of motion over a time interval, so it cannot be a scalar. Therefore, these three options are vector quantities and not correct answers to the question.

Common Pitfalls:
Students sometimes confuse velocity with speed and think average velocity is scalar; however, speed is scalar and velocity is vector. Another mistake is to assume that any quantity associated with electricity or magnetism is scalar, but fields and moments are typically vector quantities. To improve accuracy, always look at the standard definitions and whether direction is an essential part of the description.

Final Answer:
Power is the only scalar quantity among the given options.