Question

A proton falls through a distance 3.5 cm in a uniform electric field of magnitude 2×10^4 NC^-1 . The acceleration of the proton is__________ ms^-2 ( Mass of the proton is 1.6 × 10^-27 kg )​

Answer 1

ATQ, S=1.5cm=1.5×10

−2

m

u=0m/s

m

e

: mass of electron =9.10×10

−31

Kg

m

p

: mass of proton =1.672×10

−27

Kg

from coloumb's force,

F

=q

E

and given

E

=2×10

4

N/c

force proton

F

(+)

=1.6×10

−19

×2×10

4

=3.2×10

−19

N

force on electron,

F

(−)

=−1.6×10

−19

×2×10

4

=−3.2×10

−15

N

From Newton's Second law,

F

=m

a

for proton, a

(+)

=

m

p

F

(+)

=1.913×10

12

m/s

2

for electron, a

(−)

=

m

e

F

(−)

=−0.35×10

16

m/s

2

from equ of motion, S=ut+

2

1

at

2

⟶(1)

ATQ, The direction of the field was reversed, hence we will ignore the sign convention for acceleration.

∴ Substituting values in equ (1) for proton,

1.5×10

−2

=

2

1

×1.913×10

12

×t

2

1.568×10

−14

=t

2

⇒t=1.252×10

−7

seconds

Substituting values in equ(1) for electron,

1.5×10

−2

=

2

1

×3.5×10

15

×t

2

0.857×10

−17

=t

2

⇒t

0

=2.927×10

−19

seconds

Answer 2

Given data : A proton falls through a distance 3.5 cm in a uniform electric field of magnitude 2 * 10⁴ N/C.

To find : The acceleration of the proton ?

Solution : A/C to question;

• Electric field, E = 2 * 10⁴ N/C
• Charge on the proton, q = 1.602×10^(-19) C
• Mass of the proton, m = 1.6 * 10^(-27) kg

Here, we know downward electric field causes the proton to collapse/fall and A proton falls through a distance 3.5 cm {3.5 * 10^(-2)m} in uniform electric field.

Now,

➜ Force = mass * acceleration

➜ F = m * a

Here,

➜ Electric field of a point charge : E = F/q

∴ F = E * q

Hence,

➜ E * q = m * a

Now,

➜ E * q = m * a

➜ 2 * 10⁴ * 1.602×10^(-19) = 1.6 * 10^(-27) * a

➜ 3.204 * 10^(-15) = 1.6 * 10^(-27) * a

➜ a = 3.204 * 10^(-15)/1.6 * 10^(-27)

➜ a = 2.0025 * 10¹² m/s²

Answer : A proton falls through a distance 3.5 cm in a uniform electric field of magnitude 2 * 10⁴ N/C . The acceleration of the proton is 2.0025 * 10¹² m/s². {Mass of the proton is 1.6 × 10^(-27) kg}.

{More info :

• Protons are positively charged particles.
• They have a mass of 1.67×10^(-27)kg .
• They are present inside the nucleus.
• Proton is said to be very stable whether it's in its free state or inside the atoms. They do not decay spontaneously.
• The atomic number of an element is equal to the number of protons in the atom.
• Protons are represented as p+}