Acircular loop of radius 13 cm carries a current of 16 a. a flat coil of radius 0.63 cm, having 48 turns and a current of 1.5 a, is concentric with the loop. the plane of the loop is perpendicular to the plane of the coil. assume the loop's magnetic field is uniform across the coil. what is the magnitude of (a) the magnetic field produced by the loop at its center and (b) the torque on the coil due to the loop?

a) Bt = 7.73 * 10^-5 T

b) T = 6.94 * 10^-7 N*m

Explanation:

Step 1: Data given

Circumar loop Radius = 13 cm

Current = 16 A

Flat coil radius = 0.63 cm

48 turns

Current = 1.5 A

a) What is the magnitude of (a) the magnetic field produced by the loop at its center

Let's assume a loop concentric with a coil, the plane of the coil is perpendicular to the plane of the loop. The magnetic field due to the loop at the center of the loop can be given by:

Bt = µ0It / 2Rt

In this case we'll get:

Bt = ((4π * 10^-7 T*m/A)(16A)) /(2*0.13m)

Bt = 7.73 * 10^-5 T

b) What is the magnitude of the torque on the coil due to the loop?

The torque magnitude excreting on the coil due to the magnetic field of the loop is given by:

T = µcBtsin(∅)

with µc = the magnetic dipole moment of the coil

with ∅ = the angle between the magnetic dipole moment and the magnetic field. The magnetic dipole moment is given by:

µc = N*Ic*A

⇒ with N = the number of turns in the coil

⇒ with A =  πRc² = the area of the coil

µc =π*N*Ic*Rc²

T= π*N*Ic*Rc²*Bt(sin∅)

In this situation we'll have:

T= π*48*1.5A* (0.63 *10^-2m)²*(7.73 * 10^-5 T)*sin(90)

T = 6.94 * 10^-7 N*m

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.