One beam of electrons moves at right angles to a magnetic field. the force on these electrons is 4.9 × 10-14 newtons. a second beam travels at the same speed, but at a 30° angle with the magnetic field. what force is on these electrons?

a.(4.9 × 10-14 newtons) · tan(30°)
b.(4.9 × 10-14 newtons) · sin(30°)
c.(4.9 × 10-14 newtons) · cos(30°)
d.(4.9 × 10-14 newtons) · arctan(30°)
e.(4.9 × 10-14 newtons) · arccos(30°)

B.(4.9 × 10-14 newtons) · sin(30°)

Explanation:

The magnetic force exerted on charged particles by a magnetic field is given by

where

q is the charge

v is the speed of the charge

B is the magnetic field intensity

is the angle between the direction of v and B

The first beam moves at right angle to the magnetic field, so and the force on this beam is simply

(1)

The second beam moves at angle of . The electrons are travelling at same speed v, and the magnetic field is still the same (and the charge q is also the same, since they are electrons as well), so the magnetic force in this case is

(2)

But from the previous equation we know that

so, if we substitute into eq. (2), we find

potential energy is directly proportional to height.

more height = more potential energy.

greatest increase in height = greatest increase in potential energy

where are the points with the greatest increase in height ?

has to be c-e or d-e .

  the grams     of oxygen gas   that can be produced     is 20.6   grams of o₂

calculation

2liclo₃ →   2 licl + 3 o₂

step 1:   find the moles of liclo₃

moles = mass÷ molar mass

from periodic table the molar mass of liclo₃ =6.9 +35.5   +(16 x3) =90.4 g/mol

moles=38.7 g÷90.4 g/mol=0.4281   moles

step 2:   use the   mole ratio   to calculate the moles of o2

from equation above, liclo₃: o₂   is 2: 3  

therefore the moles of   o₂=0.4281 moles x3/2 =0.6422   moles

step 3: find mass   of o₂

mass= moles x molar mass

from periodic table the   molar mass of   o₂ = 16 x2= 32 g/mol

mass=0.6422   moles   x   32 g/mol = 20.6 grams of o₂