At what radial distance r from the center of a toroid of 150 windings does the magnitude of the magnetic field equal that found inside a solenoid that has 550 turns per meter of length? assume that the current is the same through both devices.

express your answer with the appropriate units.
express your answer with the appropriate units.

The required radial distance from the center of the toroid is -

r = 4.34 cm

Explanation:

We know that magnetic field inside a solenoid is given by -

B = μni

where 'μ' is the magnetic permeability , 'n' is the number of turns per unit length , 'i' is the current passing through solenoid.

given n = 550  turns/meter

We know that magnetic field inside a toroid is -

B = μ××i [Current is same in both the devices] , where 'N' is the total number of turns in the toroid and 'r' is the radial distance from the center of the toroid.

Given N = 150.

Equating the two magnetic fields , we get -

μni = μ××i

∴

Substituting the values we get -

r = 0.0434 m = 4.34 cm

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.