A muon is a particle with a mass of 1.88 · 10−28 kg and a charge q = −e. What is the magnitude of the acceleration of a muon in an electric field E = 5.23 · 10−6 N/C?

Question

A muon is a particle with a mass of 1.88 · 10⁻²⁸ kg and a charge q = −e. What is the magnitude of the acceleration of a muon in an electric field E = 5.23 · 10⁻⁶ N/C?

Answer 1

To start this problem, we need the formula of electric field and that of electric force given below:

Electric Field (E) = (KQ)/(r) Electric Force (F) = (KQq)/(r)

As we can see from the derived equations, they are very similar, with only the term q being left out of the electric field equation.

Thus, we can come up with the new equation: F = Eq

To solve for force, we will plug in the given value for the electric field into the formula and we will also plug in the charge of an electron (as indicated by q = -e) (-1.6 x 10^-19 C) into the equation as shown below:

F = (5.23 x 10^-6 N/C)(-1.6 x 10^-19 C)

F = -8.37 x 10^-25 N

Now, to find acceleration, we will need to remember Newton's 2nd law, which is the formula: F = ma

F = -8.37 x 10^-25 N = (1.88 x 10^-28 kg) (a)

Acceleration = -4451.06 (m)/(s²)