We are given the following information:
• Length of the conducting rod, L=0.45 mL = 0.45 \, \text{m}
• Mass of the rod, m=60 g=0.06 kgm = 60 \, \text{g} = 0.06 \, \text{kg}
• Current through the rod, I=5.0 AI = 5.0 \, \text{A}
• Gravitational acceleration, g=9.8 m/s2g = 9.8 \, \text{m/s}^2
Let's solve the problem step by step.
Part (a): Magnetic field to make tension zero
To make the tension in the wires zero, the magnetic force on the rod must balance the weight of the rod. This is because when the rod is under the influence of a magnetic force, it will experience a force that could counteract the gravitational force.
The magnetic force on the conducting rod in a magnetic field is given by the formula:
FB=ILBF_B = I L B
where:
• FBF_B is the magnetic force,
• II is the current through the rod,
• LL is the length of the rod,
• BB is the magnetic field.
The weight of the rod is given by:
W=mgW = mg
where:
• WW is the weight of the rod,
• mm is the mass of the rod,
• gg is the acceleration due to gravity.
To make the tension zero, the magnetic force must balance the weight of the rod:
ILB=mgI L B = mg
Substitute the given values:
5.0 A×0.45 m×B=0.06 kg×9.8 m/s25.0 \, \text{A} \times 0.45 \, \text{m} \times B = 0.06 \, \text{kg} \times 9.8 \, \text{m/s}^2 2.25B=0.5882.25 B = 0.588 B=0.5882.25=0.261 TB = \frac{0.588}{2.25} = 0.261 \, \text{T}
So, the magnetic field required to make the tension zero is 0.261 T0.261 \, \text{T}.
Part (b): Total tension if current is reversed
If the direction of the current is reversed, the magnetic force on the rod will reverse its direction as well. However, the weight of the rod will still act downward.
The magnetic force will now act in the opposite direction, and so will tend to pull the rod in the opposite direction. The magnetic force, therefore, still balances the weight of the rod, but since the current direction is reversed, the direction of the force changes, resulting in an increase in the tension in the wires.
The total tension in the wires will be the sum of the magnetic force and the weight. This is because the magnetic force now opposes the gravitational force:
T=FB+WT = F_B + W
From part (a), we already know the magnetic force FB=0.588 NF_B = 0.588 \, \text{N}, and the weight W=0.588 NW = 0.588 \, \text{N}.
So, the total tension is:
T=0.588 N+0.588 N=1.176 NT = 0.588 \, \text{N} + 0.588 \, \text{N} = 1.176 \, \text{N}
Final Answer:
• (a) The magnetic field required to make the tension zero is 0.261 T0.261 \, \text{T}.
• (b) The total tension in the wires if the current is reversed is 1.176 N1.176 \, \text{N}.
