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 in this scenario, you can use the right-hand rule. When the thumb of your right hand points in the direction of the electric current (i) and your fingers curl in the direction of the magnetic field (B), the palm of your hand will face in the direction of the magnetic force (FB).
In this case, the magnetic force (FB) is in the negative x-direction. To achieve this, you can point your thumb in the positive y-direction and curve your fingers downwards in the negative z-direction. Therefore, according to the right-hand rule, the magnetic field (B) must be in the negative z-direction.
So, the correct answer is e) negative z-direction.
2) To calculate the ratio of the magnetic field inside solenoid 1 to the magnetic field inside solenoid 2, you can use the formula for the magnetic field inside a solenoid:
B = (μₒ * N * I) / L
where B is the magnetic field, μₒ is the permeability of free space (constant), N is the number of turns of the solenoid, I is the current flowing through the solenoid, and L is the length of the solenoid.
Let's compare the two solenoids:
For solenoid 1: N₁ = 15N, I₁ = 7I
For solenoid 2: N₂ = N, I₂ = I
We need to calculate B₁ / B₂:
(B₁ / B₂) = [(μₒ * N₁ * I₁) / L] / [(μₒ * N₂ * I₂) / L]
= [(N₁ * I₁) / (N₂ * I₂)]
Substituting the given values:
(B₁ / B₂) = [(15N) * (7I)] / [N * I]
= 15 * 7
= 105
Therefore, the ratio of the magnetic field inside solenoid 1 to the magnetic field inside solenoid 2 is 105.
Hence, the correct answer is a) 105.