Force = q V X B
where V and B are vectors and "x" denotes the vector "cross product". For an electron, q is negative. In (a), V is towards the east (unit vector i) and B is down (unit vector -k). The vector V x B is north (according to he right hand rule) and the minus sign of q makes the force to the south.
(b) The acceleration is F/m, in the same direction as the force F. m is the mass of the electron
The electrons in the beam of a television tube have a kinetic energy of 2.10 10-15 J. Initially, the electrons move horizontally from west to east. The vertical component of the earth's magnetic field points down, toward the surface of the earth, and has a magnitude of 5.00 10-5 T.
(a) In what direction are the electrons deflected by this field component?
due south (correct)
due west
due east
due north
(b) What is the acceleration of an electron in part (a)?
I have tried everything and all of my answers are wrong. In part a the correct answer is due south. Please help with part (b).
5 answers
I am so confused! Can you please define "cross product". I interpret it to mean that you multiply the value of V and B. Obviously this is incorrect.
Will my answer have a negative value because of the mass of the electron?
This is what I did:
Acceleration = [(q V X B)/ m
(-1.60x10^-19)(6.789932x10^12)(X)(5.00x10^-5)] / 9.11x10^-31)
I got the value of V from the equation for KE
KE = 1/2m V^2
2.10x10^-5 J = 1/2(9.11x10^-31)V^2
(2.10x10^-5)/(4.555x10^-31) = V^2
4.610318x10^25 = V^2
6.789932x10^12 = V
Will my answer have a negative value because of the mass of the electron?
This is what I did:
Acceleration = [(q V X B)/ m
(-1.60x10^-19)(6.789932x10^12)(X)(5.00x10^-5)] / 9.11x10^-31)
I got the value of V from the equation for KE
KE = 1/2m V^2
2.10x10^-5 J = 1/2(9.11x10^-31)V^2
(2.10x10^-5)/(4.555x10^-31) = V^2
4.610318x10^25 = V^2
6.789932x10^12 = V
Your answer for the magnitude of the acceleration will not have a negative sign. However, you must specify the direction.
You should be familiar with the term "cross prodct" if you are studying the forces of magnetic fields. It is a vector concept and vectors are usually tught in introductory calculus and analytic geometry. Awhat a cross product A X B means is |A|*|B| sin theta, where |A| amd |B| are the magnitudes of two vectors and theta is the angle between them. The direction of A X B is perpendicular to the plane containing A and B
You should be familiar with the term "cross prodct" if you are studying the forces of magnetic fields. It is a vector concept and vectors are usually tught in introductory calculus and analytic geometry. Awhat a cross product A X B means is |A|*|B| sin theta, where |A| amd |B| are the magnitudes of two vectors and theta is the angle between them. The direction of A X B is perpendicular to the plane containing A and B
I suggest you learn more about vector cross products here, if a description is not in your textbook somewhere:
http://en.wikipedia.org/wiki/Cross_product
http://en.wikipedia.org/wiki/Cross_product
The electrons in the beam of a television tube have a kinetic energy of
2.40*10-15 J. Initially, the electrons move horizontally from west to east. The
vertical component of the earth’s magnetic field points down, toward the
surface of the earth, and has a magnitude of 2.00*10-5 T. (a) in what
direction are the electrons deflected by this field component? (b) What is the
acceleration of an electron in part (a)?
2.40*10-15 J. Initially, the electrons move horizontally from west to east. The
vertical component of the earth’s magnetic field points down, toward the
surface of the earth, and has a magnitude of 2.00*10-5 T. (a) in what
direction are the electrons deflected by this field component? (b) What is the
acceleration of an electron in part (a)?
1 answer