1)A wire is carrying a current, i, in the positive y-direction. The wire is located in a uniform magnetic field, B, oriented in such a way that the magnetic force on the wire is maximized. The magnetic force acting on the wire, FB, is in the negative x direction. What is the direction of the magnetic field?

a) positive x-direction
b)negative x-direction
c)negative y-direction
d) positive z-direction
e) negative z-direction

I'm not really sure how the right hand rule 3 works for this but I just put my thumb in the direction of i and my fingers were curving downwards, so I pick e) but I'm not sure.

2. Two solenoids have the same length, but solenoid 1 has 15 times the number of turn, 1/9 the radius and 7 times the current of solednoid 2. Calculate the ratio of the magnetic field inside solenoid 1 to the magnetic field inside solenoid 2.
a) 105
b) 123
c) 144
d) 168
e) 197

I'm really not sure how to do this, I started by just plugging random numbers in for the equation B=(mu_naught*i)/(2pi*r)
I just plugged 2 for N, 3 for r, and 5 for i, and calculated the magnetic field for both and divided B of s2 by B of s1 and got 1.05E-3, I thought that that was right since I looked on the back of the book and the answer is in fact a) but I later noticed that I was using the equation for a toroid not a solenoid, since radius doesn't even affect the B of solenoids. I did the same thing with the equation B=(mu_naught*i)*(N/L) and (with L=15) got a number that wasn't on the choices, so I really don't know how to do this. Help please.

1) To determine the direction of the magnetic field, you can use the right-hand rule for the magnetic force (also known as the Lorentz force). Here's how to apply it:

- Align your thumb in the direction of the current, i, which is in the positive y-direction.
- Extend your fingers as if gripping the wire (perpendicular to your thumb).
- Your fingers will curve downwards due to the magnetic force.
- The negative x-direction corresponds to the direction of your palm.

Therefore, the correct answer is b) negative x-direction.

2) To calculate the ratio of the magnetic field inside solenoid 1 to the magnetic field inside solenoid 2, you can use the equation for the magnetic field inside a solenoid:

B = μ₀ * (N/L) * i,

where B is the magnetic field, μ₀ is the permeability of free space, N is the number of turns, L is the length of the solenoid, and i is the current.

Let's assume the magnetic field inside solenoid 1 is B₁ and inside solenoid 2 is B₂.

Given:

- Solenoid 1 has 15 times the number of turns compared to solenoid 2: N₁ = 15N₂.
- Solenoid 1 has 1/9 the radius of solenoid 2: R₁ = (1/9)R₂.
- Solenoid 1 has 7 times the current compared to solenoid 2: i₁ = 7i₂.

Since the lengths of both solenoids are the same, we can cancel out L from the equation.

Now, we can calculate the ratio B₁/B₂:

B₁/B₂ = (μ₀ * (N₁/L) * i₁) / (μ₀ * (N₂/L) * i₂)
= (N₁ * i₁) / (N₂ * i₂).

Using the given ratios, we substitute the values:

B₁/B₂ = (15N₂ * 7i₂) / (N₂ * i₂)
= 105.

So, the ratio of the magnetic field inside solenoid 1 to the magnetic field inside solenoid 2 is 105 (answer choice a)).