Question
Question: A straight horizontal conducting rod of length 0.45m and mass 60g is suspended by two vertical wires...
A straight horizontal conducting rod of length 0.45m and mass 60g is suspended by two vertical wires at its ends. A current of 5.0A is set up in the rod through the wires.
a. What magnetic field should be set up normal to the conductor in order that the tension in the wires is zero?
b. What will be the total tension in the wires if the direction of current is reversed keeping the magnetic field the same as before? (Ignore the mass of the wires.) g=9.8ms−2
Solution
Hint: We will first acknowledge all the values given to us in the question and then we will solve both the parts one by one respectively keeping in mind the situations given in each part. We will apply the formula of magnetic force in the first part and then solve it further. We will find out the value of total tension in the second part by acknowledging that the magnetic force will add up to the weight if the direction of the current is reversed. Refer to the solution below.
Formula used: Fm=il×B, T=iBl+mg.
Complete step-by-step answer:
Length of the rod as per given in the question = 0.45m
Mass of the rod as per given by the question = 60g = 0.06kg
Value of the current passing through the rod = 5A
As we already know that for a conductor in a magnetic field, the magnetic force is considered to be-
⇒Fm=il×B
We know that the angle between them is 90 degrees. So, if we solve this cross product, we will get-
⇒Fm=ilB
part-A
Basically, the magnetic force calculated above should always balance the weight of the rod. Thus-
⇒ilB=mg ⇒B=ilmg
Now, substituting the value of mass, gravity, length and the current. We will get-
⇒B=ilmg ⇒B=5×0.450.06×9.8 ⇒B=5×45×106×98 ⇒B=2250588 ⇒B=0.26T
Hence, the value of the magnetic field required is 0.26T.
Part-B
If the direction of current is reversed, the magnetic force will add up to the weight. Hence, the total tension will be-
⇒T=iBl+mg
We were clear in part A that ilB=mg, which brings us to the solution-
⇒T=mg+mg ⇒T=2mg ⇒T=2×0.06×9.8 ⇒T=1.176N
Hence, the value of total tension after the direction of the current is reversed will be 1.176N.
Note: Magnetic force, attraction and repulsion which occurs due to the motion between electrically charged particles. The magnetic force between two motion charges can be described as the influence that a magnetic field produced by the other exerts on each charge.