This article is to solve vector spherical coordinates. Solve vector spherical coordinates is nothing but solving problems under spherical coordinate with the help of the tutors. Tutor vista tutor have many highly qualified tutors in online. A quantity which has magnitude and direction is a vector. There are three methods to describe a vector. Specific lengths, direction, angles, projections or components are the methods. Below we can see about solve vector spherical coordinates.
Solve Vector Spherical Coordinates
From this system any point as the point of intersection of the spherical surface (radius r = constant) conical surface (theta phitheta and phi by dr, rd theta and dphi .The element sides are dr,rd theta and rsin theta dphi . = constant). A differential volume element is obtained in spherical coordinate. This happens by increasing r value,
The differential length dl = sqrt(dr^2+(rd theta)^2+(rsin theta dphi)^2)
The differential areas ds = dr.rd theta = rdrd theta
= dr.rsin theta dphi = r sin theta dphi dr
= rd theta. rsin theta dphi = r2sin2 theta d theta dphi
The differential volume dv = dr.rd theta.rsin theta dphi
dv = r2sin theta dphi dr.
So spherical co ordinates = (r, theta, phi)
Solve Vector Spherical Coordinates
A vector in cartesian co-ordinate system can be converted to spherical coordinate.
Conversion of cartesian to spherical system
The Cartesian co-ordinates is (x,y,z). This cartesian coordinate is converted into spherical co-ordinates ( r, theta, phi )
Given Transform
x r = sqrt (x2+y2+z2)
y theta = cos-1(z/(sqrt(x2+y2+z2))) = cos-1(z/r)
z phi = tan-1(y/x)
Problem 1: Convert the cartesian coordinates x = 2, y = 1, z = 3 into spherical co-ordinates.
Given Transform
x = 2 r = sqrt (x2+y2+z2)
= sqrt (4+1+9)
= sqrt (14) = 3.74
y = 1 cos-1(z/r) = cos-1(3/sqrt(14)) = 36.7°
z = 3 phi = tan-1(y/x) tan-1(1/2)26.56°
Spherical co- ordinates are (3.74, 36.7°, 26.56°)
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