ANS-1) ANS-2) ANS-3) ANS-4) yer al -y-eg. If $ D dl = 3 is true on a surface, which of the following is absolutely true? UCH.uzeyin The surface where the linear path is determined is PEC (perfect electric conductor) The sum of the voltage drops over the line-path is zero mengi r igi yuzey ..... There is charge on the surface area where the linear path is determined. ANS-5) Çizgisting, Mittun. ...ir. There is at least one point on the surface area where the linear path is determined, where the tangent component of E is not zero. YUK YUK There is no charge on the surface area where the linear path is determined. HUR

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Gradient of a Scalar Field

Consider a room or a place where the temperature is denoted by a scalar field T, such that at each point (x, y, z), the temperature is given as T(x, y, z). It is independent of time, in which the temperature rises most quickly. The gradient of T will show the direction at that point by moving away from (x, y, z). How far will the rise in temperature in that direction be determined by the gradient magnitude? Consider a surface that has a height above sea level at point (x, y) which is given by H(x, y). At that point, pointing in the direction of the steepest slope or grade is the gradient of H. The magnitude of the gradient of the vector gives the steepness of the slope at that point. How a scalar field changes in another direction can be measured by the gradient by taking a dot product rather than just the direction of the greatest change?