Question

Choose the correct statement from the following options:
A. Temperature is a scalar but temperature gradient is vector
B. Velocity of the body is a vector but velocity of light is a scalar
C. Electric intensity and electric current density are vectors
D. All of the above

Answer 1

Hint: Temperature is a scalar quantity, but the temperature differential is a vector, since the vector is the gradient of every scalar quantity. A body's velocity is a vector because it has both magnitude and direction, but light velocity is a scalar because the vector addition theorem does not hold true for light velocity.

Complete answer:
-Temperature is a scalar but temperature gradient is a vector, as gradient of any scalar quantity is a Vector. A body's velocity is a vector since it has both magnitude and direction, but light velocity is a scalar since the vector addition rule is not constant for light velocity. A charged body's electrical intensity is nothing but electrical field intensity and its direction is determined by the direction of force that will result in a unit positive test charge due to that body.
-Electrical current density is current perpendicularly going through a unit cross-section field; the current density direction is along the current direction.Temperature is a scalar, but temperature gradient is a vector and body velocity is a vector, but light velocity is a scalar and vectors are electrical strength and electrical current density.

Hence all the options (A), (B) and (C) are right. So option (D) is the correct answer.

Note:A charged body's electric strength is nothing but the intensity of the electric field and its direction is determined by the direction of force that a positive unit test charge would feel because of that body.