A velocity selector consists of electric field $\overrightarrow{E}=E\widehat{k}$ and magnetic field $\overrightarrow{B}=B\widehat{j}$ with B = 12 mT. The value of E required for and electron of energy 728 eV moving along the positive x-axis to pass undeflected is:

(Given. Mass of electron = 9.1 × 1031kg)

<p><math><mrow><mi>K</mi><mi>E</mi><mo>=</mo><mn>7</mn><mn>2</mn><mn>8</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>6</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>1</mn><mn>9</mn></mrow></msup><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>×</mo><mn>9</mn><mo>.</mo><mn>1</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>3</mn><mn>1</mn></mrow></msup><mo>×</mo><msup><mrow><mi>V</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></p><p>V = 16 × 106 m/s</p><p>For Lorentz force to be zero</p><p>eE = eVB</p><p><math><mrow><mo>⇒</mo><mi>E</mi><mo>=</mo><mi>v</mi><mi>B</mi><mo>=</mo><mn>1</mn><mn>6</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>6</mn></mrow></msup><mo>×</mo><mn>1</mn><mn>2</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math></p><p>= 192 × 103 V/m</p>

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