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.
Duplicate post. See answer to the same question posted later.
1) To determine the direction of the magnetic field, you can use the right-hand rule for the cross product of vectors. In this case, you have the current vector and the magnetic force vector, and you want to find the direction of the magnetic field vector.
Using the right-hand rule, you would point your right thumb in the direction of the current (positive y-direction) and then curve your fingers in the direction of the magnetic force (negative x-direction). Your fingers would then point towards the negative z-direction. Therefore, 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 = mu_0 * N * i / L
where B is the magnetic field, mu_0 is the permeability of free space, N is the number of turns, i is the current, and L is the length.
Given that solenoid 1 has 15 times the number of turns (N1 = 15N2), 1/9 the radius (r1 = (1/9)r2), and 7 times the current (i1 = 7i2), we can plug these values into the formula.
The ratio of the magnetic fields is then:
B1 / B2 = (mu_0 * N1 * i1 / L) / (mu_0 * N2 * i2 / L)
= (mu_0 * 15N * 7i) / (L * mu_0 * N * i)
= 15 * 7
= 105
Therefore, the ratio of the magnetic field inside solenoid 1 to the magnetic field inside solenoid 2 is 105, which corresponds to option a).