Author: Physics Notebook

Calculate The Solid Angle Subtended By A Ring Element.

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Physics Notebook

Let us consider a sphere of radius R and a ring element PQTS of thickness PQ on the surface of the shere. OA is normal through the centre of the ring element. Here and the angular width of the ring element is . Let be the radius of the ring QT, so . Now the…
Determine The Surface Area Of A Sphere Of Radius ‘r’ By Using The Spherical Polar Co-Ordinate System.

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Physics Notebook

Surface area of a sphere: Let us consider a sphere of radius r with centre at O. Let, PQRS be an elementary surface of area on the surface of the sphere. For each point on this area element, r is constant but and are variable. So the area element is given by, , the direction…
Calculate The Solid Angle Subtended At The Centre Of The Sphere By The Surface Of The Sphere.

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Physics Notebook

Solid angle subtended at the centre of the sphere: Let us consider a sphere of radius r, Now we want to calculate the solid angle at the centre O of the sphere by the total surface area of the sphere. Let’s consider, an elementary area dA on the surface of the sphere. So the solid…
Show That Only One Type Of Area Element In The Spherical Polar Co-Ordinate System Subtends A Solid Angle At The Origin.

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Physics Notebook

In spherical polar co-ordinate system, there are three surface elements and . [To know about the three types of area elements and their values (CLICK HERE)] Now in case of the surface element , is constant but and are variable. And the magnitude is Here, the area element is perpendicular to the radial vector…
Derive An Expression For The Solid Angle In The Spherical Polar Co-Ordinate System.

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Physics Notebook

Solid angle in the spherical polar co-ordinate system: In spherical polar co-ordinate system, there are three area elements and , out of which only the area element subtends a solid angle at the centre . [To know about the three types of area elements (CLICK HERE)] The area element is perpendicular to the direction of…
A particle moves in a plane in such a way that its distance from the origin remains constant. What is the radial component of the velocity?

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Physics Notebook

We know that when a particle is moving along a curve in a plane, then the transverse component of velocity is . [To know the derivation of the radial component of velocity (CLICK HERE) ] Since the particle moves in such a way that the distance from the origin of the particle remains constant, this…
The trajectory of a particle moving in a plane in a straight line passing through the origin. What is the transverse component of velocity?

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Physics Notebook

Transverse component of velocity of a particle moving along a straight line in a plane: We know that when a particle is moving along a curve in a plane, then the transverse component of velocity is . [To know the derivation of the transverse component of velocity (CLICK HERE) ] Since, here the particle is…
The Cartesian Co-Ordinates Of A Point Are (1, 0, 1). Find The Spherical Polar Co-Ordinates Of That Point.

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Physics Notebook

Let us consider the spherical polar co-ordinate of the point are . Now given that the Cartesian co-ordinate of that point are, We know that, and, So the spherical polar co-ordinates of the given point are [ To know the relations between the cartesian co-ordinates and the spherical polar co-ordinates (CLICK HERE) ]
The Cartesian Co-Ordinates Of A Point Are (1, 0, 0). Find The Spherical Polar Co-Ordinates Of That Point.

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Physics Notebook

Let us consider the spherical polar co-ordinate of the point are . Now given that the Cartesian co-ordinate of that point are, We know that, and, So the spherical polar co-ordinates of the given point are [ To know the relations between the cartesian co-ordinates and the spherical polar co-ordinate (CLICK HERE) ]
Calculate The Spherical Polar Co-Ordinates Of A Point Whose Cartesian Co-Ordinates Are (1, 0, √3).

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Physics Notebook

Let us consider the spherical polar co-ordinate of the point are . Now given that the Cartesian co-ordinate of that point are, We know that, and, So the spherical polar co-ordinates of the given point are [ To know the relation between cartesian co-ordinates and the spherical polar co-ordinates (CLICK HERE) ]