Question:
An electric field of \(1000 \, V/m\) and a perpendicular magnetic field act on a moving electron to produce no net force. If the speed of the electron is \(2.5 \, km/s\), then the magnitude of the magnetic field is:
An electric field of \(1000 \, V/m\) and a perpendicular magnetic field act on a moving electron to produce no net force. If the speed of the electron is \(2.5 \, km/s\), then the magnitude of the magnetic field is:
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For zero net force, velocity must satisfy \(v = E/B\) in perpendicular E and B fields.
Updated On: Jul 18, 2026
- 0.4 T
- 0.25 T
- 0.6 T
- 0.75 T
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The Correct Option is A
Solution and Explanation
Step 1: Condition for no net force on moving charge.
A charged particle moving in perpendicular \(\mathbf{E}\) and \(\mathbf{B}\) fields experiences net force: \[ \mathbf{F} = q (\mathbf{E} + \mathbf{v} \times \mathbf{B}) \] No net force implies: \[ q\mathbf{E} + q \mathbf{v} \times \mathbf{B} = 0 \quad \Rightarrow \quad E = v B \]
Step 2: Convert velocity to SI units.
Given \(v = 2.5 \, km/s = 2500 \, m/s\)
Step 3: Solve for magnetic field.
\[ B = \frac{E}{v} = \frac{1000}{2500} = 0.4 \, T \]
Step 4: Check direction.
Velocity is perpendicular to magnetic field, satisfying cross product condition.
Step 5: Verification.
\(\mathbf{v} \times \mathbf{B} = 2500 \cdot 0.4 = 1000 \, V/m = E\) ✓
Step 6: Final conclusion.
\[ \boxed{0.4 \, T} \]
A charged particle moving in perpendicular \(\mathbf{E}\) and \(\mathbf{B}\) fields experiences net force: \[ \mathbf{F} = q (\mathbf{E} + \mathbf{v} \times \mathbf{B}) \] No net force implies: \[ q\mathbf{E} + q \mathbf{v} \times \mathbf{B} = 0 \quad \Rightarrow \quad E = v B \]
Step 2: Convert velocity to SI units.
Given \(v = 2.5 \, km/s = 2500 \, m/s\)
Step 3: Solve for magnetic field.
\[ B = \frac{E}{v} = \frac{1000}{2500} = 0.4 \, T \]
Step 4: Check direction.
Velocity is perpendicular to magnetic field, satisfying cross product condition.
Step 5: Verification.
\(\mathbf{v} \times \mathbf{B} = 2500 \cdot 0.4 = 1000 \, V/m = E\) ✓
Step 6: Final conclusion.
\[ \boxed{0.4 \, T} \]
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