Question

The distance between the plates of a parallel plate condenser is 4 m m 4 mm and potential difference between them is 200 v 200 v. the condenser is placed in a magnetic filed b b. an electron is projected vertically upwards parallel to the plates with a velocity of 10 6 m / s 106m/s. the electron passes undeviated through the space between the plates. the magnitude and direction of magnetic filed b will be

Answer 1

Given:

The distance between the plates of a parallel plate condenser is 4 mm and potential difference between them is 200 V the condenser is placed in a magnetic filed B an electron is projected vertically upwards parallel to the plates with a velocity of 10^6 m/s. The electron passes undeviated through the space between the plates.

To find:

Magnitude and direction of magnetic field.

Calculation:

The electrostatic force on the electron will be equal and opposite to the magnetic force acting on the moving electron. Hence the electron moves undeviated parallel to the plate of the capacitor.

$\rm{ \therefore \: magnetic \: force = electrostatic \: force}$

$\rm{ = > \: qvB = qE}$

$\rm{ = > \: vB = E}$

$\rm{ = > \: vB = \dfrac{V}{length} }$

$\rm{ = > \: {10}^{6} \times B = \dfrac{200}{4 \times {10}^{ - 3} } }$

$\rm{ = > \: B = 0.5 \times {10}^{ - 1} }$

$\rm{ = > \: B = 5 \times {10}^{ - 2} \: W {m}^{ - 2} }$

Direction of the magnetic field will be into the plane of the paper perpendicular to the plates of the Capacitor..