Question:
A conducting rod $AC$ of length $4 l$ is rotated about appoint $O$ in a uniform magnetic field $\vec{B}$ directed into the paper. $ AO=l $ and $ OC=3l $ then:
A conducting rod $AC$ of length $4 l$ is rotated about appoint $O$ in a uniform magnetic field $\vec{B}$ directed into the paper. $ AO=l $ and $ OC=3l $ then:
Updated On: Jun 23, 2023
- $V_{A}-V_{O}=\frac{B \omega l^{2}}{2}$
- $V_{O}-V_{C}=\frac{9}{2} B \omega l^{2}$
- $V_{A}-V_{C}=4 B \omega l^{2}$
- $V_{C}-V_{O}=\frac{9}{2} B \omega l^{2}$
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The Correct Option is A
Solution and Explanation
Given, length of rod $=4 l$; magnetic field $=B$
If $\omega=$ angular velocity
$
\omega=\frac{v}{l} \quad(v=v e l o c i t y) .
$
Now, small emf (d ) due to small element de is:
$d \epsilon=B vdl =B wl d l$
On integrating it upto length ' $l$ ' of rod, the emf $(epsilon)$ will be: $\varepsilon=B \omega \int_{0}^{l} l d l$
$\varepsilon=\frac{B \omega l^{2}}{2}=$ potential difference b/w $A \& 0$.
Thus,
$
V_{A}-V_{0}=\frac{B \omega l^{2}}{2}
$
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Concepts Used:
Magnetism & Matter
Magnets are used in many devices like electric bells, telephones, radio, loudspeakers, motors, fans, screwdrivers, lifting heavy iron loads, super-fast trains, especially in foreign countries, refrigerators, etc.
Magnetite is the world’s first magnet. This is also called a natural magnet. Though magnets occur naturally, we can also impart magnetic properties to a substance. It would be an artificial magnet in that case.
Read More: Magnetism and Matter
Some of the properties of the magnetic field lines are:
- The lines and continuous and outside the magnet, the field lines originate from the North pole and terminate at the South pole
- They form closed loops traversing inside the magnet.
- But here the lines seem to originate from the South pole and terminate at the North pole to form closed loops.
- More number of close lines indicate a stronger magnetic field
- The lines do not intersect each other
- The tangent drawn at the field line gives the direction of the field at that point.