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# Assertion : An electron is not deflected on passing through a certain region of space. This observation confirms that there is no magnetic field in that region. Reason : The deflection of electron depends on angle between velocity of electron and direction of magnetic field A. If both assertion and reason are true and the reason is the correct explanation of the assertion. B. If both assertion and reason are true but reason is not the correct explanation of the assertion. C. If the assertion is true but the reason is false. D. If the assertion is false but the reason is True.

Last updated date: 18th May 2024
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Hint: In order to solve this question, we will first check the correctness of both the given assertion and reason statements and then we will check whether the reason is the correct explanation of assertion or not.

Formula used:
The expression of Lorentz force is given as,
$F = q(v \times B)$ Here, $q$ is the charge on the particle, $v$ is the velocity of the charged particle and $B$ is the magnetic field.

Complete step by step solution:
We have given the assertion statement as An electron is not deflected on passing through a certain region of space. This observation confirms that there is no magnetic field in that region, so when an electric charge enters a field and if it’s not deflected it does not confirm that there is no magnetic field because if the velocity of the particle is parallel to the magnetic field then Lorentz force on the particle is
$F = q(v \times B) \\ \Rightarrow F = qvB\sin \theta$
As the velocity of the particle is parallel to the magnetic field therefore $\sin \theta =0$.
$\Rightarrow F = 0$
Since, the angle between velocity and the magnetic field is zero, so our assertion is false.

Now, the reason statement is given to us that The deflection of an electron depends on the angle between the velocity of the electron and the direction of the magnetic field and yes, the reason is true as the deflection of an electron depends upon the angle between velocity and magnetic field as we have written in Lorentz force as $F = q(v \times B)$. But, the reason statement does not say how the deflection depends upon the angle so the reason is correct but it does not explain our assertion.

Hence, the correct answer is option D.

Note:It should be remembered that in the formula of Lorentz for velocity v and magnetic field B are used in vector form and the product between them is vector product also, remember the trigonometric values as $\sin {0^o} = 0.$