Author: Physics Notebook
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Define And Explain Solid Angle, What Are Its Dimensions? What Are Its Units?
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Solid Angle: The solid angle subtended by a surface at a point is measured by the ratio of the normal component of the area of the surface to the square of the distance of the surface from the point. Let us consider be the solid angle at a point O, subtended by the area .…
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Derive An Expression For Acceleration Of A Particle In Cylindrical Polar Co-Ordinate System.
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Let us consider a point P in cylindrical co-ordinate system, having cylindrical co-ordinates . The cartesian co-ordinates of the point P is . Let’s draw a vertical line PQ on the X-Y plane, which is parallel to the z-axis, as shown in Fig.1. OQ is represented by , which makes an angle with the X-axis.…
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Derive The Expression For Velocity In Cylindrical Polar Co-Ordinate System.
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Let us consider a point P in cylindrical co-ordinate system, having cylindrical co-ordinates . The cartesian co-ordinates of the point P is . Let’s draw a vertical line PQ on the X-Y plane, which is parallel to the z-axis, as shown in Fig.1. OQ is represented by , which makes an angle with the X-axis.…
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Express The Unit Vectors In Cylindrical Polar Co-Ordinate System In Terms Of The Unit Vectors In Spherical Polar Co-Ordinate System.
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Let us consider a point P in cylindrical polar co-ordinate system, having cylindrical co-ordinates . The cartesian co-ordinates of the point P is . Let’s draw a vertical line PQ on the X-Y plane, which is parallel to the z-axis, as shown in Fig.1. OQ is represented by , which makes an angle with the…
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Derive An Expression For The Volume Element In Spherical Polar Co-Ordinate System.
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Let us consider a very small volume element PQRSS’P’Q’R as shown in Fig.1. The lower surface PQRS of this volume element lies on the surface of the sphere of radius and the parallel surface P’Q’R’S’ lies on the surface of the sphere of radius . Since the angles and and radial extension are very small,…
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Derive An Expression For Area Element In Spherical Polar Co-Ordinate System.
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Let us consider a very small volume element PQRSS’P’Q’R as shown in Fig.1. The lower surface PQRS of this volume element lies on the surface of the sphere of radius and the parallel surface P’Q’R’S’ lies on the surface of the sphere of radius . Since the angles and and radial extension are very small,…
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Derive An Expression For The Line Element In Spherical Polar Co-Ordinate System.
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Line element in the spherical polar co-ordinate system: Let us consider a very small volume element PQRSS’P’Q’R as shown in Fig.1. The lower surface PQRS of this volume element lies on the surface of the sphere of radius and the parallel surface P’Q’R’S’ lies on the surface of the sphere of radius . Since the…
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Find The Value Of Area Element In Plane Polar Co-Ordinate System.
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Area element in plane polar co-ordinate system: Let us consider a point having plane polar co-ordinates with respect to the origin as shown in the figure 1. Now the vector is increased to through a small increment , in the direction of unit vector . here the angular increment is over the angle in the…
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Find The Value Of Line Element In Plan Polar Co-Ordinate.
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Line element in plan polar co-ordinate system: Let us consider two points and in a plane polar co-ordinate system with respect to the origin O as shown in Fig. 1. The polar co-ordinate of is and the polar co-ordinate of is . Now and . Therefore, or, Here the vector is a line element. If…
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Find The Expression For The Area Element In Rectangular Cartesian Co-Ordinate System.
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Area element in rectangular cartesian co-ordinate system: Let us consider a parallelogram represented by the vectors and as shown in the adjoining figure 1. So the area vector of the parallelogram is given by, , since the area is a vector product of two vectors, so the area is a vector quantity and the direction…