A nonuniform electric field is given by the expression vector e = ay i + bz j + cx k, where a, b, and c are constants. determine
the electric flux (in the +z direction) through a rectangular surface in the xy plane, extending from x = 0 to x = w and from y = 0 to y = h. (use any variable or symbol stated above as necessary.)
1 answer:
The flux through a surface is given by the scalar product of the field strength and the area
of the surface.
As the rectangular surface is in xy plane the flux corresponding to x and y component of field will be zero (parallel to the surface) and the flux through the surface is only due to z component of the field.
Because flux is the dot product of Electric field and area vector. So, parallel to surface is 0.
So,
The z component of the field is varying with x only and directly proportional to x coordinate. (cx k)
Consider an infinitely thin strip of the surface at a distance x from y axis of thickness dx as in figure. Field at this strip will have magnitude c*x and will be normal to the surface hence the flux through this strip will be given by :
As the rectangular surface is in xy plane the flux corresponding to x and y component of field will be zero (parallel to the surface) and the flux through the surface is only due to z component of the field.
Because flux is the dot product of Electric field and area vector. So, parallel to surface is 0.
So,
The z component of the field is varying with x only and directly proportional to x coordinate. (cx k)
Consider an infinitely thin strip of the surface at a distance x from y axis of thickness dx as in figure. Field at this strip will have magnitude c*x and will be normal to the surface hence the flux through this strip will be given by :
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Answer:
the charge of the particle is 2.47 x 10⁻¹⁹ C
Explanation:
Given;
mass of the particle, m = 6.64 x 10⁻²⁷ kg
velocity of the particle, v = 8.7 x 10⁵ m/s
strength of the magnetic field, B = 1.3 T
radius of the circle, r = 18 mm = 1.8 x 10⁻³ m
The magnetic force experienced by the charge is calculated as;
F = ma = qvB
where;
q is the charge of the particle
a is the acceleration of the charge in the circular path
Therefore, the charge of the particle is 2.47 x 10⁻¹⁹ C