A 0.2 kg conductor of length 0.8 m carries 2 ampere current to the right in a magnetic field. What is the magnitude and the direction of the magnetic field acting on the conductor if the net force on the rod is zero? (Assume that the rod is hung by two insulating supports.)
Selected Answer:
1.2 is the magnitude
Correct Answer:
Correct
Since the net force is zero, the weight of the rod should be balanced upward by the magnetic force on the rod. According to the right-hand rule, the magnetic field should be directed into the plane of paper and perpendicular to the direction of the current. Hence the weight of the rod should be balanced by the magnetic force.
To find the magnitude and direction of the magnetic field acting on the conductor, we can use the formula for the magnetic force on a current-carrying conductor in a magnetic field.
The formula for the magnetic force is given by:
F = BIL
Where:
F is the magnetic force,
B is the magnetic field strength,
I is the current flowing in the conductor,
L is the length of the conductor.
In this case, the net force on the rod is zero, so we can conclude that the magnetic force on the conductor is equal and opposite to the gravitational force acting on it.
The gravitational force can be calculated using the formula:
F_gravity = mg
Where:
m is the mass of the conductor and
g is the acceleration due to gravity.
Since the net force on the conductor is zero, the magnetic force is equal in magnitude to the gravitational force:
F_magnetic = F_gravity
Therefore,
BIL = mg
We can rearrange the formula to solve for the magnetic field strength B:
B = mg / (IL)
Plugging in the values given in the problem:
m = 0.2 kg
g = 9.8 m/s^2
I = 2 A
L = 0.8 m
B = (0.2 kg)(9.8 m/s^2) / (2 A)(0.8 m)
B = 0.098 N / (1.6 A x m)
B = 0.06125 T (T refers to Tesla, the SI unit of magnetic field strength)
So, the magnitude of the magnetic field acting on the conductor is 0.06125 Tesla.
The direction of the magnetic field can be determined using the right-hand rule. Curl your right-hand fingers in the direction of the current flow (to the right), and your thumb will point in the direction of the magnetic field. In this case, the magnetic field points downwards.
Therefore, the magnitude of the magnetic field is 0.06125 Tesla, and the direction is downward.
To find the magnitude and direction of the magnetic field acting on the conductor, we can use the following equation:
F = BIL
Where:
F is the force acting on the conductor,
B is the magnetic field,
I is the current flowing through the conductor, and
L is the length of the conductor.
In this case, we are given that the net force on the rod is zero, which means the force acting on the conductor (F) is zero.
So, we can rearrange the equation to solve for the magnetic field (B):
B = F / (IL)
Since F is zero, the magnetic field must also be zero.
Therefore, in this scenario, the magnitude of the magnetic field acting on the conductor is zero, and its direction is undefined.
if there is no net force, the magnetic force BIL equals the weight, M g.
Therefore
B = M g/(I L)
= 0.2*9.8/(2.0*0.8) = 12.25 T
The direction of the B field must produce an upward force. Use the right hand rule.