Sure! Let's walk through the step-by-step solution to find the magnetic field strength given the following information:
- Force ([tex]\( F \)[/tex]) = [tex]\( 1.5 \times 10^2 \)[/tex] N
- Charge ([tex]\( q \)[/tex]) = [tex]\( 1.4 \times 10^{-7} \)[/tex] C
- Velocity ([tex]\( v \)[/tex]) = [tex]\( 1.3 \times 10^6 \)[/tex] m/s
- Angle ([tex]\( \theta \)[/tex]) = [tex]\( 75^\circ \)[/tex]
The formula to find the magnetic field strength ([tex]\( B \)[/tex]) when a charged particle is moving in a magnetic field is given by:
[tex]\[ F = q \cdot v \cdot B \cdot \sin(\theta) \][/tex]
We can rearrange this formula to solve for [tex]\( B \)[/tex]:
[tex]\[ B = \frac{F}{q \cdot v \cdot \sin(\theta)} \][/tex]
Let's calculate this step by step:
1. Convert the angle from degrees to radians:
[tex]\[ \theta = 75^\circ = \frac{75 \times \pi}{180} \text{ radians} \][/tex]
2. Calculate [tex]\( \sin(\theta) \)[/tex]:
[tex]\[ \sin(75^\circ) \][/tex]
3. Plug in the values:
[tex]\[ B = \frac{1.5 \times 10^2 \text{ N}}{(1.4 \times 10^{-7} \text{ C}) \times (1.3 \times 10^6 \text{ m/s}) \times \sin(75^\circ)} \][/tex]
4. Simplify the expression and compute the result.
By following these steps, we obtain:
[tex]\[ B \approx 853.2495992390795 \text{ T} \][/tex]
Therefore, the magnetic field strength is approximately [tex]\( 853.2495992390795 \)[/tex] T. Given the provided choices:
1. [tex]\( 8.2 \times 10^2 \)[/tex] T
2. [tex]\( 8.5 \times 10^2 \)[/tex] T
3. [tex]\( 3.2 \times 10^3 \)[/tex] T
4. [tex]\( 6.4 \times 10^{10} \)[/tex] T
The closest match to our calculated value is:
[tex]\[ 8.5 \times 10^2 \text{ T} \][/tex]
So, the correct answer is:
[tex]\[ \boxed{8.5 \times 10^2 \text{ T}} \][/tex]
