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 using B=(1/r)Sqrt(2mV/q^2) 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)

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!

What answer do you get when you calculate? Am I doing something wrong in my calculations?

I get 1.3E7 m/s

According to my homework this is incorrect too. What could be wrong.

Let's break down the problem and go through the calculation step by step to find where the mistake might be occurring.

1. We are given the following information:
- Potential difference (V) = 6.4 kV = 6.4 × 10^3 V
- Charge of an electron (q) = 1.60218 × 10^-19 C
- Mass of an electron (m) = 9.10939 × 10^-31 kg
- Radius of the circular path (r) = 5.1 cm = 5.1 × 10^-2 m

2. We need to find the magnetic field strength (B) in units of T (Tesla) experienced by the electron.

3. To calculate the velocity of the electron, we can use the equation relating potential difference and kinetic energy:
V = (1/2)mv^2
Rearranging for v, we get:
v = sqrt((2V) / m)
Plugging in the values, we have:
v = sqrt((2 × 6.4 × 10^3) / (9.10939 × 10^-31))
v ≈ 3.187 × 10^7 m/s

4. Now, we can calculate the magnetic field strength using the formula relating magnetic field, velocity, charge, and radius:
B = (m/q) * (v/r)
Plugging in the values, we have:
B = (9.10939 × 10^-31 / 1.60218 × 10^-19) * (3.187 × 10^7 / 5.1 × 10^-2)
B ≈ 1.75882 × 10^11 T

So, the correct answer for the magnetic field strength experienced by the electron in a circular path of radius 5.1 cm is approximately 1.75882 × 10^11 T.