hard_revenge
11-12-2006, 02:27 AM
السلام عليكم ورحمه الله وبركاته انا كنت لقيت شويه المسائل دى وقلت ارفعه علشان اللى عاوز يتتدرب على المسائل وانا هرفعهم على ثلاث مرات ان شاء الله علشان هما كتار شويتين واتمنى انهم يعجبوكم:
A charge +Q is situated at (-a,0,0) and a charge -2Q is situated at (a,0,0). Is there a point in space where E = 0?
A point charge of 5 nC is located at the point (2,-2,3)m and another point charge of 3 nC is located at the point (-3,1,2)m. Find the force F of these charges on a charge of 2 nC at (4,4,4)m. Express F in terms of its rectangular components and in terms of magnitude and unit vector.
A point charge is situated at each corner of an equilateral triangle. If the charges are 3 nC each,, is there a point (not at infinity) at which the total force on a test charge is zero? Deteremine the coordinates of this points if it exists.
A charge +Q is located at the point (0,0,d/2). Another charge –Q is located at the point (0,0,-d/2). The two charges of equal magnitude but opposite sign seperated by the distance d constitute an electric dipole of dipole moment P = qd az. Find the electric field E in terms of P at: a- any point (0,0,z) on the z axis for which z >> d, b- any point (r,θ,φ) in space for which r >> d.
A field is given in spherical coordinates as E = [cos θ / r2 ] ar + [sin θ /r] a . Express E in terms of rectangular coordinates x, y, z, ax, ay, and az and find E at (1,2,4).
The charge density varies with radius r in a cylindrical coordinate system as ρ = q /(r2 + a2)2, where q and a are constants. Within what distance from the z axis does half the total charge lie?
If the volume charge density varies linearly with radius, ρ = ρoa/r, where ρo and a are constants, and spherical coordinate system is assumed, find the total charge lying within: a- the sphere r ≤ a, b- the cone r ≤ a, 0 ≤ θ ≤ π/3.
An infinite line charge of charge density qL = 2 nC/m lies along the x axis in fre space, while two point chages of 8 nC are located at (0,0,1) and (0,0,-1). Find E at (2,3,-4). To what value should qL be changed to cause E to be zero at (0,0,3)?
The semi-infinite line, z ≥ 0, x = 0, y = 0, carries a uniform charge density of 15 nC/m. Determine E at the point (1,2,3) in free space.
The portion of the z axis -2 ≤ z ≤ +2 carries a nonuniform charge of density qL = 10 z nC/m for 0 ≤ z ≤ 2, qL = -10 z nC/m for 0 ≥ z ≥ -2 and qL = 0 elsewhere . Determine E at the points (0,0,4) and (0,4,0) in free space.
المجموعه الثانيه
A uniform line charge of density 2.357 nC/m lies along the x axis and a uniform sheet of charge is located at y = 5 m. Along the line y = 3 m, z = 3 m the electric field E has only a z component. What is the surface charge density on the sheet?
A thin cicular ring of radius a lies in the horizontal plane z = 0 with its center at the origin. The ring carries a uniform charge of density ρs. Find the electric field at a point (0,0,z) on the z axis. Derive an integral expression for the field at any point P in space of spherical polar coordinates (r, θ,φ).
The circular disc r ≤ a, z = 0 carries a charge of density ρs = 10 /r nC/m2. Determine the electric field E at any point on the z axis.
A uniform line charge of ρl = 2π nC/m lies along the y axis, while uniform surface charge densities of +0.1 and -0.1 nC/m2 exist on the planes z = 3 m and z = -4 m, respectively. Find E at the point P(1,-7,2). At which point is E the negative of the field at P?
Given the field E = (2x - 1) ax + (4 -2y) ay, find the general form of the steam line and plot that line passing throgh the point (1,3,6).
An electric field is given by E = coshx siny ax + sinhx cosy ay. Find E at the point P of cartezian coordinates (0,π/3,0). Determine the equation of the steam line through P and the intersection of this steam line with the straight lines x = 1, x = 2, and x =5.
Given a scalar function V = 50x2yz + 20 y2, find : (a) grad V at the point P(1,2,3), (b) unit normal to the surface V = const at the point P, (c) equation of the tangent plane to the surface V = const at the point P.
An electric field E = 25 aρ + 12 aφ – 20 az at the point P of cylindrical coordinates (8,60o,5). Find the component of E that is perpendicular to the cylinder ρ = 8 and the component that is tangent to the same cylinder at P.
Find the flux of the vector D = 8x2 y2 ax + 4x2 y ay leaving the surface of the cube: -0.5≤ x ≤ 0.5, -0.5≤ y ≤ 0.5, -0.5≤ z ≤ 0.5.
For the scalar fuction V = 1/ [ (x + 1 )2 + y2 ]1/2 , what is the shape of the surface V = const.? Determine unit normal to this surface at the point P(2,4,2). Determine the flux of the vector E = - grad V over the surface V = const. through the point P between the planes z = 0 and z = 5.
واتمنى ان شاء الله انهم يعجبوكم وطبعا بين كل مساله والتانيه مسافه واضحه وشكرا سلاموز
A charge +Q is situated at (-a,0,0) and a charge -2Q is situated at (a,0,0). Is there a point in space where E = 0?
A point charge of 5 nC is located at the point (2,-2,3)m and another point charge of 3 nC is located at the point (-3,1,2)m. Find the force F of these charges on a charge of 2 nC at (4,4,4)m. Express F in terms of its rectangular components and in terms of magnitude and unit vector.
A point charge is situated at each corner of an equilateral triangle. If the charges are 3 nC each,, is there a point (not at infinity) at which the total force on a test charge is zero? Deteremine the coordinates of this points if it exists.
A charge +Q is located at the point (0,0,d/2). Another charge –Q is located at the point (0,0,-d/2). The two charges of equal magnitude but opposite sign seperated by the distance d constitute an electric dipole of dipole moment P = qd az. Find the electric field E in terms of P at: a- any point (0,0,z) on the z axis for which z >> d, b- any point (r,θ,φ) in space for which r >> d.
A field is given in spherical coordinates as E = [cos θ / r2 ] ar + [sin θ /r] a . Express E in terms of rectangular coordinates x, y, z, ax, ay, and az and find E at (1,2,4).
The charge density varies with radius r in a cylindrical coordinate system as ρ = q /(r2 + a2)2, where q and a are constants. Within what distance from the z axis does half the total charge lie?
If the volume charge density varies linearly with radius, ρ = ρoa/r, where ρo and a are constants, and spherical coordinate system is assumed, find the total charge lying within: a- the sphere r ≤ a, b- the cone r ≤ a, 0 ≤ θ ≤ π/3.
An infinite line charge of charge density qL = 2 nC/m lies along the x axis in fre space, while two point chages of 8 nC are located at (0,0,1) and (0,0,-1). Find E at (2,3,-4). To what value should qL be changed to cause E to be zero at (0,0,3)?
The semi-infinite line, z ≥ 0, x = 0, y = 0, carries a uniform charge density of 15 nC/m. Determine E at the point (1,2,3) in free space.
The portion of the z axis -2 ≤ z ≤ +2 carries a nonuniform charge of density qL = 10 z nC/m for 0 ≤ z ≤ 2, qL = -10 z nC/m for 0 ≥ z ≥ -2 and qL = 0 elsewhere . Determine E at the points (0,0,4) and (0,4,0) in free space.
المجموعه الثانيه
A uniform line charge of density 2.357 nC/m lies along the x axis and a uniform sheet of charge is located at y = 5 m. Along the line y = 3 m, z = 3 m the electric field E has only a z component. What is the surface charge density on the sheet?
A thin cicular ring of radius a lies in the horizontal plane z = 0 with its center at the origin. The ring carries a uniform charge of density ρs. Find the electric field at a point (0,0,z) on the z axis. Derive an integral expression for the field at any point P in space of spherical polar coordinates (r, θ,φ).
The circular disc r ≤ a, z = 0 carries a charge of density ρs = 10 /r nC/m2. Determine the electric field E at any point on the z axis.
A uniform line charge of ρl = 2π nC/m lies along the y axis, while uniform surface charge densities of +0.1 and -0.1 nC/m2 exist on the planes z = 3 m and z = -4 m, respectively. Find E at the point P(1,-7,2). At which point is E the negative of the field at P?
Given the field E = (2x - 1) ax + (4 -2y) ay, find the general form of the steam line and plot that line passing throgh the point (1,3,6).
An electric field is given by E = coshx siny ax + sinhx cosy ay. Find E at the point P of cartezian coordinates (0,π/3,0). Determine the equation of the steam line through P and the intersection of this steam line with the straight lines x = 1, x = 2, and x =5.
Given a scalar function V = 50x2yz + 20 y2, find : (a) grad V at the point P(1,2,3), (b) unit normal to the surface V = const at the point P, (c) equation of the tangent plane to the surface V = const at the point P.
An electric field E = 25 aρ + 12 aφ – 20 az at the point P of cylindrical coordinates (8,60o,5). Find the component of E that is perpendicular to the cylinder ρ = 8 and the component that is tangent to the same cylinder at P.
Find the flux of the vector D = 8x2 y2 ax + 4x2 y ay leaving the surface of the cube: -0.5≤ x ≤ 0.5, -0.5≤ y ≤ 0.5, -0.5≤ z ≤ 0.5.
For the scalar fuction V = 1/ [ (x + 1 )2 + y2 ]1/2 , what is the shape of the surface V = const.? Determine unit normal to this surface at the point P(2,4,2). Determine the flux of the vector E = - grad V over the surface V = const. through the point P between the planes z = 0 and z = 5.
واتمنى ان شاء الله انهم يعجبوكم وطبعا بين كل مساله والتانيه مسافه واضحه وشكرا سلاموز