A wire has a length of 4.52 x 10-2 m and is used to make a circular coil of one turn. There is a current of 7.94 A in the wire. In the presence of a 8.04-T magnetic field, what is the maximum torque that this coil can experience?
@ Megan
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Torque = (# of turns)(current)(Area)((magnetic field)(sin(angle)))
Area = (circumference)^2 / (4π)
circumference is distance around the edge of a circle.
Torque = (1)(7.94)(((4.52 x 10^-2)^2)/(4π))(8.04 sin(90))
=(7.94)(((4.52 x 10^-2)^2)/(4π))(8.04)
=(7.94)((.0452)^2/(4π))(8.04)
= .0103787 N*m
WHEN YOU CALCULATE AREA ON YOUR CALCULATOR MAKE SURE TO PUT BRACKETS AROUND THE 4π.
****THIS --> (.0452)^2/(4π)
NOT THIS --> (.0452)^2/4π
IF YOU DON'T ADD BRACKETS THEN IT WILL NOT GIVE YOU THE CORRECT AREA.
A 45 turn coil of radius 5.1 cm rotates in a uniform magnetic field having a magnitude of 0.49 T. If the coil carries a current of 40 mA, find the magnitude of the maximum torque exerted on the coil.
Torque = (the number of turns)(current)(Area)((magnetic field)(sin(angle)))
Area = π × r^2
the angle is the angle between the normal to the plane of the coil and the magnetic field.
Torque = (45)(40)(π(5.1)^2)(0.49 sin(90))
Maximum torque occurs when the magnetic force is perpendicular to the normal (which is sin(90)= 1
= (45)(40)(π(5.1)^2)(0.49)
= 72070.71158 N*m
To find the maximum torque that the coil can experience, we need to use the formula for torque in a magnetic field.
The formula for torque (τ) experienced by a current-carrying coil in a magnetic field is given by:
τ = NIABsinθ
Where:
- τ is the torque
- N is the number of turns in the coil (in this case, it is 1 turn)
- I is the current flowing through the wire (7.94 A)
- A is the area of the coil (which we need to calculate)
- B is the magnetic field strength (8.04 T)
- θ is the angle between the magnetic field and the plane of the coil (90° in this case, as the field is perpendicular to the coil)
To calculate the area (A) of the coil, we can use the formula for the circumference of a circle:
Circumference = 2πr
Given the length of the wire (4.52 x 10^-2 m), we can equate it to the circumference (C) of the circle:
C = 2πr
Since we know C and want to find A, we can rearrange the formula:
C = 2πr
A = πr^2
Now we have all the values we need to calculate the torque.
Substituting the given values into the formula:
τ = 1 * (7.94 A) * (πr^2) * (8.04 T) * sin(90°)
Since sin(90°) = 1, we can simplify the equation:
τ = 1 * (7.94 A) * (πr^2) * (8.04 T) * 1
Now we can calculate the torque.