We have two solenoids: solenoid 2 has twice the diameter, half the length, and twice as many turns as solenoid 1. The current in solenoid 2 is three times that in solenoid 1. How does the field B2 at the center of solenoid 2 compare to B1 at the center of solenoid 1?

the field at the center of solenoid 2 is 12 times the field at the center of solenoid 1.

Explanation:

Recall that the field inside a solenoid of length L, N turns, and a circulating current I, is given by the formula:

Then, if we assign the subindex "1" to the quantities that define the magnetic field () inside solenoid 1, we have:

notice that there is no dependence on the diameter of the solenoid for this formula.

Now, if we write a similar formula for solenoid 2, given that it has :

1) half the length of solenoid 1 . Then

2) twice as many turns as solenoid 1. Then

3) three times the current of solenoid 1. Then

we obtain:

b. lifting dumbbell weight at 20-degree angle from the body after a 45-degree angle

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