An electron is accelerated by a 6.4 kV potential difference. The charge on an electron is 1.60218 × 10^−19 C and its mass is 9.10939 × 10^−31 kg. How strong a magnetic field must be experienced by the electron if its path is a circle of radius 5.1 cm?
Answer in units of T.
*** I tried usind B=(1/r)Sqrt(2mV/q) and I'm not sure what I am doing wrong.
centripetal force= magnetic force
m v^2/r=Bqv
B= m/q * v/r
you have to change the potential difference to velocity first
6.4E3*q=1/2 m v^2
or v=sqrt 2*6.4E3*2/m
1/r * sqrt (m*2*6.4E3/q^2)
So it appears you need to square q in the sqrt sign. Check my work.
What am I doing wrong? Sqrt (9.10939x10^-31)x(2)x(6400)/(1.60218x10^-19)sqrd =673966.5256
ans * (1/.051) = 13215029.91 Wrong answer. I have entered four wrong answers. I can not enter another wrong answer and pass this homework. pls help!
To find the strength of the magnetic field experienced by the electron, we can use the formula for the centripetal force acting on a charged particle moving in a magnetic field.
The centripetal force is provided by the magnetic force, given by the equation:
F = qvB
Where:
F is the centripetal force,
q is the charge of the electron (1.60218 × 10^−19 C),
v is the velocity of the electron, and
B is the magnetic field strength.
The electron's velocity can be determined using the equation for the kinetic energy:
KE = 0.5mv^2
Given:
Potential difference (V) = 6.4 kV = 6.4 × 10^3 V,
Charge of the electron (q) = 1.60218 × 10^−19 C,
Mass of the electron (m) = 9.10939 × 10^−31 kg, and
Radius of the circular path (r) = 5.1 cm = 5.1 × 10^−2 m.
First, we need to find the velocity of the electron:
The potential difference (V) is given by:
V = KE/q
Rearranging the equation above, we can solve for the kinetic energy:
KE = V * q
Substituting the given values:
KE = (6.4 × 10^3 V) * (1.60218 × 10^−19 C) = 1.02667 × 10^−15 J
Next, we can calculate the velocity:
KE = 0.5mv^2
Rearranging the equation above, we can solve for v:
v = sqrt((2 * KE) / m)
Substituting the given values:
v = sqrt((2 * 1.02667 × 10^−15 J) / (9.10939 × 10^−31 kg)) = 5.858 × 10^6 m/s
Now, we can calculate the magnetic field strength using the centripetal force equation:
F = qvB
Rewriting the equation to solve for B:
B = F / (qv)
The centripetal force can be calculated using:
F = mv^2 / r
Substituting the given values:
F = (9.10939 × 10^−31 kg) * (5.858 × 10^6 m/s)^2 / (5.1 × 10^−2 m) = 9.827 × 10^−12 N
Finally, we can calculate the magnetic field strength:
B = (9.827 × 10^−12 N) / ((1.60218 × 10^−19 C) * (5.858 × 10^6 m/s)) ≈ 3.20 × 10^−3 T
Therefore, the strength of the magnetic field experienced by the electron is approximately 3.20 × 10^−3 T.