an electron having energy 500eV emerges out of a region containing magnetic field at right angle to the motion having flux density 10 x 10^-5Wbm and strikes on a screen. if effective length of magnetic regionbis 20mm and distance of screen from magnetic field is 175mm find deflection on screen
Answers
Answer:
So does the magnetic force cause circular motion? Magnetic force is always perpendicular to velocity, so that it does no work on the charged particle. The particle’s kinetic energy and speed thus remain constant. The direction of motion is affected, but not the speed. This is typical of uniform circular motion. The simplest case occurs when a charged particle moves perpendicular to a uniform B-field, such as shown in Figure 2. (If this takes place in a vacuum, the magnetic field is the dominant factor determining the motion.) Here, the magnetic force supplies the centripetal force Fc = mv2/r. Noting that sin θ = 1, we see that F = qvB.
Diagram showing an electrical charge moving clockwise in the plane of the page. Velocity vectors are tangent to the circular path. The magnetic field B is oriented into the page. Force vectors show that the force on the charge is toward the center of the charge’s circular path as the charge moves.
Figure 2. A negatively charged particle moves in the plane of the page in a region where the magnetic field is perpendicular into the page (represented by the small circles with x’s—like the tails of arrows). The magnetic force is perpendicular to the velocity, and so velocity changes in direction but not magnitude. Uniform circular motion results.
Because the magnetic force F supplies the centripetal force Fc, we have
q
v
B
=
m
v
2
r
.
Solving for r yields
r
=
m
v
q
B
.
Here, r is the radius of curvature of the path of a charged particle with mass m and charge q, moving at a speed v perpendicular to a magnetic field of strength B. If the velocity is not perpendicular to the magnetic field, then v is the component of the velocity perpendicular to the field. The component of the velocity parallel to the field is unaffected, since the magnetic force is zero for motion parallel to the field. This produces a spiral motion rather than a circular one.
EXAMPLE 1. CALCULATING THE CURVATURE OF THE PATH OF AN ELECTRON MOVING IN A MAGNETIC FIELD: A MAGNET ON A TV SCREEN
A magnet brought near an old-fashioned TV screen such as in Figure 1 (TV sets with cathode ray tubes instead of LCD screens) severely distorts its picture by altering the path of the electrons that make its phosphors glow. (Don’t try this at home, as it will permanently magnetize and ruin the TV.) To illustrate this, calculate the radius of curvature of the path of an electron having a velocity of 6.00 × 107 m/s (corresponding to the accelerating voltage of about 10.0 kV used in some TVs) perpendicular to a magnetic field of strength B = 0.500 T (obtainable with permanent magnets).
A bar magnet with the north pole set against the glass of a computer monitor. The magnetic field lines are shown running from the south pole through the magnet to the north pole. Paths of electrons that are emanating from the computer monitor are shown moving in straight lines until they encounter the magnetic field of the magnet. At that point, they change course and spiral around the magnetic field lines and toward the magnet.
Figure 1. Side view showing what happens when a magnet comes in contact with a computer monitor or TV screen. Electrons moving toward the screen spiral about magnetic field lines, maintaining the component of their velocity parallel to the field lines. This distorts the image on the screen.
Strategy
We can find the radius of curvature r directly from the equation
r
=
m
v
q
B
, since all other quantities in it are given or known.
Solution
Using known values for the mass and charge of an electron, along with the given values of v and B gives us
r
=
m
v
q
B
=
(
9.11
×
10
−
31
kg
)
(
6.00
×
10
7
m/s
)
(
1.60
×
10
−
19
C
)
(
0.500
T
)
=
6.83
×
10
−
4
m
or
r = 0.683 mm.
Discussion
The small radius indicates a large effect. The electrons in the TV picture tube are made to move in very tight circles, greatly altering their paths and distorting the image.
Explanation:
its very help full