A horizontal rod with a length of 0.250 is mounted on a balance and carries a current. At the location of the rod a uniform horizontal magnetic field has a magnitude of 6.70×10−2 and direction perpendicular to the rod. The magnetic force on the rod is measured by the balance and is found to be 0.190 .

To find the current flowing through the rod, we need to use the formula for the magnetic force on a current-carrying wire in a magnetic field.

The formula is given by:

F = I * L * B * sin(θ),

where:
F is the magnetic force,
I is the current,
L is the length of the rod,
B is the magnetic field strength,
θ is the angle between the current direction and the magnetic field direction.

In this case, the rod is placed horizontally, the magnetic field is also horizontal and perpendicular to the rod, and the force is measured as 0.190 N. Therefore, the angle θ between the current and the magnetic field is 90 degrees, which means sin(θ) = 1.

The length of the rod is given as 0.250 m, and the magnetic field strength is given as 6.70×10−2 T.

So, we can rearrange the formula to solve for the current I:

I = F / (L * B * sin(θ)).

Substituting the given values:

I = 0.190 N / (0.250 m * 6.70×10−2 T * 1).

Calculating this gives the value of the current flowing through the rod.