Question

The electric field between the plates of a cathode ray oscillograph is 1.2 x 10⁴ N/C. What deflection would an electron experience if it enters at right angles to the field with kinetic energy of 2 keV, the length of the assembly
being 1.5 cm ?​

Answer 1

Answer:

Deflection y=eEx24(K) where K is kinetic energy.

Answer 2

Question↝

The electric field between the plates of a cathode ray oscillograph is 1.2 x 10⁴ N/C. What deflection would an electron experience if it enters at right angles to the field with kinetic energy of 2 keV, the length of the assembly being 1.5 cm ?

Given↝

• The electric field between the plates of a cathode ray oscillograph is 1.2 x 10⁴ N/C.

• What deflection would an electron experience if it enters at right angles to the field with kinetic energy of 2 keV.

To find↝

• Find the length of the assembly being 1.5 cm.

Solution↝

The electron moves against the electric field because it experiences a force due to the field.

$\sf \: The \: acceleration \: experienced \: by \: the \: electron \: in \: y \: direction \: is \: ay = \frac{QE}{M}$

$\sf \: Thus, by \: kinematics \: relation Δy= \frac{1}{2} ay ∆t²$

$\sf \: As \: the \: electron \: moves \: with \: a \: constant \: speed \: in \: x \: direction, Δt= \frac{∆x}{v}$

$\sf \: The \: velocity \: of \: the \: electron \: in \: terms \: of \: the \: kinetic \: energy \: is \: v= \sqrt{ \frac{2KE}{M} }$

$\sf \: Using \: the \: above \: relations \: for \: Δy, we \: have \: Δy= \frac{1}{2} \frac{qE}{m} ( \frac{∆x}{v}) {}^{2} = \frac{E∆x {}^{2} }{4 \times \frac{KE}{q} }$

$\underline{ \boxed{ \sf{ \red{Given \frac{KE}{q} = 2000 \: V \: and \: E = 1.2 × 10⁴N/C \: and \: ∆x = 1.5 \times 10 {}^{ - 2} Cm}}}}$

We get ∆y :

${ \boxed {\boxed{{ \sf\frac{1.2 \times 10 {}^{4} \times (1.5 \times 10 {}^{ - 2}) {}^{2} }{4 \times 2000} = 0.3375 \times 10 {}^{ - 3} m≈0.34mm}}}}$

More explanation↝

• Electric field, an electric property associated with each point in space when charge is present in any form.

• The magnitude and direction of the electric field are expressed by the value of E, called electric field strength or electric field intensity or simply the electric field.

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