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Assertion Maganetic field (B) and elec...

Assertion Maganetic field (B) and electric field (E) are present in a this region. Net force on a charged particle in this region is zero , if
`E=Bxx v`
Reason E/B has the dimensions of velocity.

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The correct Answer is:
To solve the problem, we need to analyze the assertion and the reason provided in the question step by step. ### Step 1: Understanding the Assertion The assertion states that the net force on a charged particle in a region with both magnetic field (B) and electric field (E) is zero if the condition \( E = B \times v \) is satisfied. ### Step 2: Force on a Charged Particle The forces acting on a charged particle (with charge \( Q \)) in an electric field and a magnetic field can be expressed as: - The electric force \( F_E = Q \cdot E \) - The magnetic force \( F_M = Q \cdot (v \times B) \) ### Step 3: Setting the Net Force to Zero For the net force to be zero, we can write: \[ F_{net} = F_E + F_M = 0 \] This implies: \[ Q \cdot E + Q \cdot (v \times B) = 0 \] Dividing through by \( Q \) (assuming \( Q \neq 0 \)): \[ E + (v \times B) = 0 \] This can be rearranged to: \[ E = - (v \times B) \] This indicates that the electric field \( E \) is equal in magnitude but opposite in direction to the magnetic force \( (v \times B) \). ### Step 4: Analyzing the Reason The reason states that \( \frac{E}{B} \) has the dimensions of velocity. To analyze this, we can look at the dimensions of electric field \( E \) and magnetic field \( B \): - The dimension of electric field \( E \) is \( [E] = \frac{ML^2}{T^3A} \) - The dimension of magnetic field \( B \) is \( [B] = \frac{ML}{T^2A} \) Calculating \( \frac{E}{B} \): \[ \frac{E}{B} = \frac{\frac{ML^2}{T^3A}}{\frac{ML}{T^2A}} = \frac{L}{T} \] This is indeed the dimension of velocity. ### Step 5: Conclusion Both the assertion and the reason are true. However, the reason does not directly explain the assertion. The assertion is about the condition for the net force to be zero, while the reason discusses the dimensional analysis of the ratio of electric and magnetic fields. ### Final Answer - Assertion: True - Reason: True - Explanation: The reason does not explain the assertion.
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