a. In FIGURE P29.76, a long, straight, current-carrying wire of linear mass density is suspended by threads. A magnetic field perpendicular to the wire exerts a horizontal force that deflects the wire to an equilibrium angle . Find an expression for the strength and direction of the magnetic field .
b. What deflects a 55 g/m wire to a 12° angle when the current is 10 A?
Give the diagram is as follows:
Given that the mass density of the wire is , the deflection angle is and a magnetic field perpendicular to the wire is applied.
The formula to calculate the mass of the wire is given by
Here, is the mass and is the length of the wire.
The formula to calculate the gravitational force of the wire is given by
Here, is the gravitational force and is the acceleration due to gravity.
Substitute the expression for the mass from equation (1) into equation (2) to obtain the gravitational force.
The formula to calculate the magnetic force exerted on the wire is given by
Here, is the magnetic force, is the current through the wire and is the magnetic field.
The formula to calculate the deflection angle of the wire is given by
Substitute the expressions for and from equations (3) and (4) respectively into equation (5) and simplify to obtain the expression for the magnetic field.
Also, using the right-hand rule, it can be said that the direction of the magnetic field is downward.
The required magnetic field is given by and the direction of the magnetic field is downward.
Given that the mass density of the wire is , the deflection angle is and the current is .
Substitute for , for , for and for into equation (6) to calculate the required magnetic field.
The required magnetic field is .
You have a horizontal cathode-ray tube (CRT) for which the controls have been adjusted such that the electron beam should make a single spot of light exactly in the center of the screen. You observe, however, that the spot is deflected to the right. It is possible that the CRT is broken. But as a clever scientist, you realize that your laboratory might be in either an electric or a magnetic field. Assuming that you do not have a compass, any magnets, or any charged rods, how can you use the CRT itself to determine whether the CRT is broken, is in an electric field, or is in a magnetic field? You cannot remove the CRT from the room.
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