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 for which the magnetic force on the wire is maximized, you can apply the right-hand rule. The right-hand rule states that if you point your thumb in the direction of the current flow (positive y-direction in this case), and then curl your fingers in the direction of the magnetic field, your palm will face the direction of the magnetic force.
Since the magnetic force (FB) is in the negative x-direction, your palm should be facing in the direction opposite to the magnetic force. In this case, it means that the magnetic field (B) should be in the positive x-direction. Therefore, the correct answer is a) positive x-direction.
2) To calculate the ratio of the magnetic field inside solenoid 1 to solenoid 2, you can use the formula for the magnetic field inside a solenoid, given by B = μ₀ * N * I / L, where μ₀ is the permeability of free space, N is the number of turns, I is the current, and L is the length.
Let's denote the subscripts "1" and "2" for solenoid 1 and solenoid 2 respectively.
Given the following ratios:
- N₁ / N₂ = 15
- r₁ / r₂ = 1/9
- I₁ / I₂ = 7 (I₁ = 7 * I₂)
The formula for the magnetic field can be rewritten as:
B₁ / B₂ = (μ₀ * N₁ * I₁) / (μ₀ * N₂ * I₂)
Since μ₀, a constant, is the same for both solenoids, we can cancel it from the equation:
B₁ / B₂ = (N₁ * I₁) / (N₂ * I₂)
Now substitute the given ratios:
B₁ / B₂ = (15 * 7) / (1 * 1)
B₁ / B₂ = 105
Therefore, the ratio of the magnetic field inside solenoid 1 to solenoid 2 is 105. Hence, the correct answer is a) 105.