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. First of all, assume the z direction is what you get as the cross product of the x and y unit vector directions, using the right hand rule. The magnetic force will be in the i X B direction, which is the direction of the cross product of y and -x unit vectors. That will be the +z direction, according to the right-hand rule
2. See http://plasma.kulgun.net/sol_page/
for the B field of a solenoid. it does not depend upon the radius. For two solenoids of the same length, the B field is proportional to the number of turns and the current. Thus solenoid 1 has a field 15 x 7 = 105 times stronger than solenoid 2.
Thank you for showing your work. Almost no one does here anymore, although we keep encouraging students to do so. When tutors are in short supply here, students who show their work or thought process are given priority.
1) To determine the direction of the magnetic field, you can use the right-hand rule. Here's how it works:
a) Point your thumb in the direction of the current (positive y-direction).
b) Curl your fingers around the wire. The direction in which your fingers curl represents the direction of the magnetic field.
Since the magnetic force on the wire is in the negative x-direction, you can conclude that the magnetic field must be in the positive z-direction (e).
1) To determine the direction of the magnetic field, we can use the right-hand rule. Here's how to apply it in this situation:
1. Point your right thumb in the direction of the current (positive y-direction in this case).
2. Curl your fingers towards the negative x-direction (since the magnetic force, FB, is in the negative x-direction).
3. Your fingers should now be pointing in the direction of the magnetic field, which is the answer you're looking for.
It seems like you followed the right-hand rule correctly and arrived at option e) negative z-direction. Well done!
2) To solve this problem, we can use the equation for the magnetic field inside a solenoid, given by B = (μ₀ * N * I) / L, where B is the magnetic field, N is the number of turns, I is the current, and L is the length.
Let's assume the magnetic field inside solenoid 1 is B₁ and inside solenoid 2 is B₂. We need to find the ratio B₁/B₂.
Given:
- Solenoid 1: N₁ = 15N₂, R₁ = 1/9R₂, I₁ = 7I₂
Let's substitute these values into the equation:
B₁ = (μ₀ * N₁ * I₁) / L
B₂ = (μ₀ * N₂ * I₂) / L
Now, simplify the equations by substituting the given relationships:
B₁ = (μ₀ * (15N₂) * (7I₂)) / L
B₂ = (μ₀ * N₂ * I₂) / L
Next, divide B₁ by B₂ to get the ratio:
(B₁ / B₂) = [(μ₀ * (15N₂) * (7I₂)) / L] / [(μ₀ * N₂ * I₂) / L]
Simplify further:
(B₁ / B₂) = [(15 * 7) * N₂ * I₂ * L] / (N₂ * I₂ * L)
Notice that the N₂, I₂, and L terms cancel out. Therefore, the final ratio B₁/B₂ depends only on the numerical values of 15 and 7:
(B₁ / B₂) = 15 * 7 = 105
Hence, the ratio of the magnetic field inside solenoid 1 to the magnetic field inside solenoid 2 is 105. The correct answer is a) 105.