Question

Which of the following quantities is a scalar?
A. Magnetic moment
B. Acceleration due to gravity
C. Electric field
D. Electrostatic potential

Answer 1

Hint: Any physical quantity having only magnitude and independent of direction is classified as a scalar quantity.

Complete step by step solution:
The magnetic moment is numerically equal to the torque acting on the magnet when held perpendicular to a uniform unit magnetic field. Its direction is given by the direction of movement of a right-handed screw when rotated in the direction of current. Thus, the magnetic moment is vector quantity.

The acceleration of a body due to gravitational force acting on it is called acceleration due to gravity. It is vector quantity, having both magnitude and direction. It is directed vertically downwards towards the center of the earth.

The electric field at a point in space due to a certain charge may be defined as the force on a unit charge positive charge placed at that point. The direction of electric field is the same as the direction of force, that is, the direction in which the positive charge placed in the field tends to move. So, an electric field having both a magnitude and a direction, is a vector quantity.

The electrostatic potential at a point in an electric field is the work done in carrying a test-charge of unit magnitude from infinity. Electric potential is scalar quantity having no direction.

Therefore, option D. is the correct answer.

Additional information:
When a scalar physical quantity is expressed from point to point in space by a continuous point function say \[\phi (x,y,z)\]which gives the value of this quantity at each point, then the function \[\phi \] is a ‘scalar field’
When a vector physical quantity is expressed from point to point in space by a continuous point function say \[\overset{\to }{\mathop{A}}\,(x,y,z)\], then the function \[\overset{\to }{\mathop{A}}\,(x,y,z)\] is a ‘vector field’

Note: The potential of an electric field is the energy characteristic. As energy is a scalar quantity having no directions, similarly electric potential is a scalar having no directions.