The problem involves a conducting rod rotating in a magnetic field, which induces an electromotive force (emf) and a current in the rod. Here's how to deduce the expression for the emf and the current:

Step 1: Understand the situation
The rod is rotating in a magnetic field, which means that different parts of the rod are moving at different speeds. The speed is proportional to the distance from the pivot point, so the speed at any point is ωr, where ω is the angular speed and r is the distance from the pivot.

Step 2: Calculate the emf
The emf induced in a small segment of the rod of length dr at a distance r from the pivot is given by dE = B ω r dr, where B is the magnetic field. To get the total emf, we integrate this expression from 0 to l (the length of the rod). This gives us E = ∫ from 0 to l (B ω r dr) = 1/2 B ω l^2.

Step 3: Calculate the current
The current I induced in the rod is given by Ohm's law, I = E/R, where R is the resistance of the rod. Substituting the expression for E from step 2, we get I = 1/2 B ω l^2 / R.

So, the emf induced in the rod is 1/2 B ω l^2 and the current induced in it is 1/2 B ω l^2 / R.

Question

The problem involves a conducting rod rotating in a magnetic field, which induces an electromotive force (emf) and a current in the rod. Here's how to deduce the expression for the emf and the current:

Step 1: Understand the situation
The rod is rotating in a magnetic field, which means that different parts of the rod are moving at different speeds. The speed is proportional to the distance from the pivot point, so the speed at any point is ωr, where ω is the angular speed and r is the distance from the pivot.

Step 2: Calculate the emf
The emf induced in a small segment of the rod of length dr at a distance r from the pivot is given by dE = B ω r dr, where B is the magnetic field. To get the total emf, we integrate this expression from 0 to l (the length of the rod). This gives us E = ∫ from 0 to l (B ω r dr) = 1/2 B ω l^2.

Step 3: Calculate the current
The current I induced in the rod is given by Ohm's law, I = E/R, where R is the resistance of the rod. Substituting the expression for E from step 2, we get I = 1/2 B ω l^2 / R.

So, the emf induced in the rod is 1/2 B ω l^2 and the current induced in it is 1/2 B ω l^2 / R.

Knowee AI · Accepted Answer

The problem involves a conducting rod rotating in a magnetic field, which induces an electromotive force (emf) and a current in the rod. Here's how to deduce the expression for the emf and the current:

Step 1: Understand the situation
The rod is rotating in a magnetic field, which means that different parts of the rod are moving at different speeds. The speed is proportional to the distance from the pivot point, so the speed at any point is ωr, where ω is the angular speed and r is the distance from the pivot.

Step 2: Calculate the emf
The emf induced in a small segment of the rod of length dr at a distance r from the pivot is given by dE = B ω r dr, where B is the magnetic field. To get the total emf, we integrate this expression from 0 to l (the length of the rod). This gives us E = ∫ from 0 to l (B ω r dr) = 1/2 B ω l^2.

Step 3: Calculate the current
The current I induced in the rod is given by Ohm's law, I = E/R, where R is the resistance of the rod. Substituting the expression for E from step 2, we get I = 1/2 B ω l^2 / R.

So, the emf induced in the rod is 1/2 B ω l^2 and the current induced in it is 1/2 B ω l^2 / R.

Conducting rod of length l with one end pivoted is rotated with a uniform angular speed omega in vertical plane normal to a uniform magnetic field B. deduce an expression for emf induced in this rod if the resistance of the rod is R . what is the current induced in it

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