1. Identify the given information: The problem involves a charged particle moving in a magnetic field. The charge of the particle is \( q = 1.6 \times 10^{-19} \) C, the mass is \( m = 9.1 \times 10^{-31} \) kg, the velocity is \( v = 5.0 \times 10^6 \) m/s, and the magnetic field strength is \( B = 0.02 \) T.
2. Use the formula for the radius of the circular path of a charged particle in a magnetic field:
\[
r = \frac{mv}{qB}
\]
3. Substitute the given values into the formula:
\[
r = \frac{(9.1 \times 10^{-31} \, \text{kg})(5.0 \times 10^6 \, \text{m/s})}{(1.6 \times 10^{-19} \, \text{C})(0.02 \, \text{T})}
\]
4. Calculate the numerator:
\[
9.1 \times 10^{-31} \times 5.0 \times 10^6 = 4.55 \times 10^{-24}
\]
5. Calculate the denominator:
\[
1.6 \times 10^{-19} \times 0.02 = 3.2 \times 10^{-21}
\]
6. Divide the numerator by the denominator:
\[
r = \frac{4.55 \times 10^{-24}}{3.2 \times 10^{-21}} = 1.421875 \times 10^{-3} \, \text{m}
\]
7. Round to two significant figures:
\[
r \approx 1.4 \times 10^{-3} \, \text{m}
\]
The radius of the circular path is \( 1.4 \times 10^{-3} \) meters.
Parent Tip: Review the logic above to help your child master the concept of math connections worksheet.
