Question

#PHYSICS


Q. A particle of charge 2μC and mass 2 mg is moving with a velocity of 5 m/s is subjected to a uniform electric field of magnitude 10 V/m for 3s. The final speed cannot be

(1) 20 m/s
(2) 25 m/s
(3) 30 m/s
(4) 35 m/s


#Answer the question with explanation.
#Spammed answer will be deleted on the spot.
​

Answer 1

Solution :-

We have :-

Charge = 2μC

= 2 × 10⁻⁶ C

Mass = 2 mg

= 2 × 10⁻⁶ kg

Velocity = 5m/s

Electric field Strength = 10 V/m

Time = 3 sec

Now First The Acceleration :-

$\rightarrow \vec{F} = q\vec{E}$

$\rightarrow \vec{F} = 2 \times 10^{-6} C \times 10 \:V/m$

$\rightarrow \vec{F} = 20 \times 10^{-6} \: N$

Now As

→ F = m × a

→ a = F ÷ m

$\rightarrow a = \dfrac{20 \times 10^{-6} \: N }{2 \times 10^{-6} \: kg}$

$\rightarrow a = 10 \: m/s^2$

Now we have got three case to get the range of possible Speed.

Case 1 :-

When angle between the acceleration and the velocity is 180°

→ | v | = | 5 - 10(3) |

→ | v | = | 5 - 30 |

→ | v | = | -25 |

→ Speed = 25 m/s

Case 2 :-

When angle between the acceleration and the velocity is 0°

→ | v | = | 5 + 10(3) |

→ | v | = | 5 + 30 |

→ | v | = | 35 |

→ Speed = 35 m/s

Case 3 :-

When angle between the acceleration and velocity is 90°

Now we will write all of our given information with directions ( in vector form )

In x - axis

Initial Velocity = 5 m/s i

Acceleration = 0

In y - axis

Initial Velocity = 0

Acceleration = 10 m/s² j

Now after 3 sec

Final velocity of x - axis

= 5 m/s i

Final velocity of y - axis

v = u + at

→ v = 0 + 10 m/s² j × 3

→ v = 30 m/s j

Now resultant of both velocity :-

$\rightarrow |\vec{R}| = \sqrt{(v_x)^2 + (v_y)^2}$

$\rightarrow |\vec{R}| = \sqrt{(5)^2 + (30)^2}$

$\rightarrow |\vec{R}| = \sqrt{25 + 900}$

$\rightarrow |\vec{R}| = \sqrt{925}$

$\rightarrow |\vec{R}| = 30.42 \: ...(approx)$

Speed = 30.42 m/s

So now we can see when we change our direction of the acceleration we get the values between [25 , 35 ] .

So from the option only 20 m/s is not coming under this region.

Hence Option (A) :- 20 m/s is Answer

Answer 2

●A particle of charge 2μC and mass 2 mg is moving with a velocity of 5 m/s is subjected to a uniform electric field of magnitude 10 V/m for 3s. The final speed cannot be 20m/s.

●The correct option is (1) 20 m/s.