Having trouble on two problems- magnetism/inductance

[Grandmas]

Not to be lazy or anything, but I was having a lot of trouble on these two physics problems for homework and don't know where to start for either.

I think for 1 I use Faraday's Law and for 2 I usee F=BILsin Theta... not sure

1. A square, single-turn coil 0.23 m on a side is placed with its plane perpendicular to a constant magnetic field. An emf of 16 mV is induced in the winding when the area of the coil decreases at a rate of 0.12 m2/s. What is the magnitude of the magnetic field?
answer in T
2. A singly charged positive ion has a mass of 2.30 10-26 kg. After being accelerated through a potential difference of 260 V, the ion enters a magnetic field of 0.530 T, in a direction perpendicular to the field. Calculate the radius of the path of the ion in the field.
answer in cm

If possible post how to do it with answer, or explain where to start and i'll try and figure it out from there. Would be much help, thanks!

 

[mezarashi]

For 1, use the relationship (Faraday's Law):

$$V = -\frac{d\phi}{dt}, where$$ $$\phi = BA$$
Hint: You know that B is constant, but the change is in A.

For 2, you can use the Lorentz force equation in conjunction with the equation for circular motion (i.e):

$$F = qv \times B = m\frac{v^2}{r}$$

 

[quicknote]

I understand that physics problems can be challenging and may require some extra effort to solve. It's important to not get discouraged and to approach these problems with a clear and logical mindset. Here are some tips to help you approach these two problems on magnetism and inductance:

1. For the first problem, remember that Faraday's Law states that the induced emf (electromotive force) in a coil is equal to the negative of the rate of change of magnetic flux through the coil. In this case, the magnetic field is constant and the area of the coil is changing, so you can use the equation: emf = -N * A * dB/dt, where N is the number of turns in the coil, A is the area of the coil, and dB/dt is the rate of change of the magnetic field. You are given all the values except for the magnetic field, so you can rearrange the equation to solve for B. Remember to convert all units to the appropriate SI units (meters, seconds, etc.) before plugging them into the equation. The answer should be in Tesla (T).

2. For the second problem, you are dealing with the motion of a charged particle in a magnetic field. The equation you mentioned, F = BILsinθ, is known as the Lorentz force law and describes the force on a charged particle moving through a magnetic field. In this case, you are given the charge of the ion, its mass, the potential difference it has been accelerated through, and the magnetic field it enters. Using the equation F = ma, you can find the acceleration of the ion. Then, using the equation for centripetal force, F = mv^2/r, you can solve for the radius of the path of the ion. Remember to convert all units to the appropriate SI units before plugging them into the equations. The answer should be in centimeters (cm).

Remember to always check your units and make sure they cancel out correctly in your equations. Also, don't hesitate to ask your teacher or classmates for help if you're still having trouble. Keep practicing and approaching problems with a logical and organized mindset, and you'll be able to tackle even the most challenging physics problems. Best of luck!