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A force of [tex]$1.5 \times 10^2 \, \text{N}$[/tex] is exerted on a charge of [tex]$1.4 \times 10^{-7} \, \text{C}$[/tex] that is traveling at an angle of [tex][tex]$75^{\circ}$[/tex][/tex] to a magnetic field.

If the charge is moving at [tex]$1.3 \times 10^6 \, \text{m/s}$[/tex], what is the magnetic field strength?

A. [tex]8.2 \times 10^2 \, \text{T}[/tex]
B. [tex]8.5 \times 10^2 \, \text{T}[/tex]
C. [tex]3.2 \times 10^3 \, \text{T}[/tex]
D. [tex]6.4 \times 10^{10} \, \text{T}[/tex]



Answer :

GinnyAnswer
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]

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