Particle that moves in a circle?

Question

1) What is the value of e/m for a particle that moves in a circle

of radius 7.0 mm in a 0.85 T magnetic field. In a separate experiment

it was found that a crossed 296 V/m electric field would make the path

straight.

Answer: 5.85 × 10^4

But that's not what I got. I did this:

mass of electron m = 9.1x10^-31

charge on electron q = 1.6x10^-19

I used qvB = (mv^2)/r

qB = (mv)/r

q/m = (v)/(rB)

q/m = (296)/[(7x10^-3)(0.85)]

q/m = 4.97x10^4

What did i do wrong?

2) The beam of elctrons goes undeflected when passing through crossed electric and magnetic fields of magnitude 1.39x10^4 V/m and 2.95x10^-3 T, respectively. What is the radius of the electron orbit, in mm, if the electric field is turned off?

Answer: 9.09

qvB = mv^2/R

qB = (mv)/R

R = (mv)/(qB)

R = [(9.1x10^-31)(1.39x10^4]/[(1.6x10^-19)(2...

= (1.2649x10^-26)/(4.72x10^-22) = 2.68x10^-5

= 2.68E-5

= 2.68E-2 mm

But that's not the answer.

Answer 1

In the first question you have incorrectly taken velocity.

You have taken velocity, v = 296, but that is electric field in volt/meter and not velocity.

You have to obtain velocity from magnetic and electric field as

v = E/B = 296 / 0.85 = 348.2

=> your answer is incorrect by a factor of 1/0.85 which on correcting gives 4.97x10^4/0.85 = 5.85x10^4 as the correct answer.

Similar mistake in the second problem also. Find velocity as

v = E/B and use in the equation.