A thin 2.84 m long copper rod in a uniform magnetic ﬁeld has a mass of 53.7 g. When the rod carries a current of 0.273 A directed perpendicular to the magnetic ﬁeld, it ﬂoats in the magnetic ﬁeld. The acceleration of gravity is 9.81 m/s2 . What is the ﬁeld strength of the magnetic ﬁeld? Answer in units of T.

Question

A thin 2.84 m long copper rod in a uniform magnetic ﬁeld has a mass of 53.7 g. When the rod carries a current of 0.273 A directed perpendicular to the magnetic ﬁeld, it ﬂoats in the magnetic ﬁeld. The acceleration of gravity is 9.81 m/s2 . What is the ﬁeld strength of the magnetic ﬁeld? Answer in units of T.

I thought I had to find force first, so I did using F=ma.
F=ma
F=53.7(9.81)
F=526.797

That didn't seem right because it was such a large number, but I continued with the problem anyway. Using the formula F=ILB (force=current*length*magnetic field vector):

F=ILB
526.797=0.273(2.84)T

And then I solved it algebraically and got 679.457 T, which as expected, wasn't the right answer.

Can anyone help?

Answer 1

The mass is .0537kg

F=ma=9.8*.0537=5.27N=
ILB=0.273(2.84)T
T=5.27/.775=6.8tesla

Answer 2

Sure! I can help you with this problem.

To find the field strength of the magnetic field, we need to use the concept of magnetic force on a current-carrying conductor in a uniform magnetic field.

Let's break down the problem step by step:

1. First, let's find the force acting on the copper rod in the magnetic field. We can use the equation F = ma, where F is the force, m is the mass of the rod, and a is the acceleration. In this case, the acceleration is due to the gravitational force, so a = g = 9.81 m/s².
Hence, F = mg = 53.7 g * 9.81 m/s².

2. Now, we need to determine the magnetic force, which is responsible for balancing the gravitational force and making the rod float. The magnetic force acting on the rod can be calculated using the equation F = ILB, where I is the current passing through the rod, L is the length of the rod, and B is the magnetic field strength.

3. Since the rod is floating, the magnetic force must be equal to the gravitational force. So we have F (gravitational force) = F (magnetic force).

Now, let's solve for the magnetic field strength:

Step 1: Calculate the force acting on the rod due to gravity:
F = mg = 53.7 g * 9.81 m/s² = 526.797 N.

Step 2: Substitute the values into the equation for the magnetic force:
526.797 N = 0.273 A * 2.84 m * B.

Step 3: Solve for B:
B = 526.797 N / (0.273 A * 2.84 m).

Calculating this, we get B ≈ 694.4 T (Tesla).

So, the field strength of the magnetic field is approximately 694.4 T.