Question:
A copper rod $AB$ of length $l$ is rotated about end A with a constant angular velocity $\omega$. The electric field at a distance $x$ from the axis of
rotation is
A copper rod $AB$ of length $l$ is rotated about end A with a constant angular velocity $\omega$. The electric field at a distance $x$ from the axis of
rotation is
Updated On: Apr 28, 2024
- $\frac{\operatorname{m} \omega^{2} x }{ e }$
- $\frac{m \omega x}{e l}$
- $\frac{m x}{\omega^{2} l}$
- $\frac{m e}{\omega^{2} x}$
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The Correct Option is A
Solution and Explanation
We know in circular motion net force acting on it must be $\frac{ mv ^{2}}{ r }$
When the rod rotates, electrons in it also rotates which produce electric field $E$ at distance $x$.
Force on the electron, $Fe = eE = m \omega^{2} x$
$\therefore Ee =\frac{ mv ^{2}}{ x } \quad( v = x \omega) $
$ Ee =\frac{ m ( x \omega)^{2}}{ x }$
$ \Rightarrow E =\frac{ m \omega^{2} x }{ e }$
When the rod rotates, electrons in it also rotates which produce electric field $E$ at distance $x$.
Force on the electron, $Fe = eE = m \omega^{2} x$
$\therefore Ee =\frac{ mv ^{2}}{ x } \quad( v = x \omega) $
$ Ee =\frac{ m ( x \omega)^{2}}{ x }$
$ \Rightarrow E =\frac{ m \omega^{2} x }{ e }$
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Concepts Used:
Electric Charge
What is Electric Charge
It is the property of subatomic particles that experiences a force when put in an electric and magnetic field. It is are of two types: Positive and Negative. It commonly carried by charge carriers protons and electrons.
Properties of Electric Charge
Various properties of charge include the following :-
- Additivity of Electric Charge
- Conservation of Electric Charge
- Quantization of Electric Charge
Types of electric charge
Two kinds of electric charges are there :-
Negative Charge - When an object has a negative charge it means that it has more electrons than protons.
Positive Charge - When an object has a positive charge it means that it has more protons than electrons.
When there is an identical number of positive and negative charges, the negative and positive charges would cancel out each other and the object would become neutral.