Question

На каком расстоянии от двояковыпуклой линзы с оптической силой 2,5 дптр надо поместить предмет, чтобы его действительное изображение получилось на расстоянии 2 м от линзы?Общее сопротивление двух последовательно соеди­ненных проводников 20 Ом, а параллельно соединен­ных этих же проводников - 4,2 Ом. Чему равно мень­шее из сопротивлений:Электрон и протон, двигаясь с одинаковыми скоростями, попадают в однородное магнитное поле перпендикулярно к линиям индукции. Сравните радиу­сы кривизны Reи Rpтраекторий электрона и прото­на.1)записать второй закон ньютона;2)записать выражение для силы Лоренца;3)записать формулу центростремительного ускорения;4)выразить радиус окружности из равенства ;5)рассчитать и сравнить радиусы.помогите пожалуйста хоть что нибудь срочно.

Answer 1

 

$D=\frac{1}{F}\\ F=\frac{1}{D}=0.4\\ \frac{1}{F}=\frac{1}{f}+\frac{1}{d}\\d=\frac{Ff}{f-F}=d=\frac{0.4*2}{2-0.4}=0.5$

 

 

$a=\frac{V^2}{R}\\a=\frac{F}{m}\\ \frac{V^2}{R}= \frac{F}{m} \\ R=\frac{V^2 m }{F}\\F=VqB\\ R=\frac{V^2 m }{qVB}\\R=\frac{Vm}{qB}$

Радиус кривизны траектории зависит от массы и заряда

 

Answer 2

Optics Problem:

To find the distance from a biconvex lens with an optical power of 2.5 diopters where an object should be placed to obtain its real image at a distance of 2 meters from the lens, we can use the lens formula:

Lens Formula: The lens formula is given by: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] where: - \( f \) = focal length of the lens - \( v \) = image distance - \( u \) = object distance

By rearranging the lens formula, we can find the object distance \( u \) in terms of the focal length and the image distance.

The focal length of the lens can be calculated using the formula: \[ f = \frac{1}{P} \] where: - \( P \) = optical power of the lens in diopters

Let's calculate the object distance \( u \) using the given values.

Using the given optical power \( P = 2.5 \, D \) and the image distance \( v = 2 \, m \), we can calculate the object distance \( u \).

Calculation:

The focal length \( f \) can be calculated using the formula: \[ f = \frac{1}{P} = \frac{1}{2.5} = 0.4 \, m \]

Now, we can use the lens formula to find the object distance \( u \): \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] \[ \frac{1}{0.4} = \frac{1}{2} - \frac{1}{u} \] \[ \frac{1}{u} = \frac{1}{2} - \frac{1}{0.4} = \frac{1}{2} - \frac{2.5}{2} = -\frac{1.5}{2} \] \[ \frac{1}{u} = -0.75 \] \[ u = -\frac{1}{0.75} = -1.33 \, m \]

The negative sign indicates that the object should be placed 1.33 meters in front of the lens.

Therefore, to obtain its real image at a distance of 2 meters from the lens, the object should be placed approximately 1.33 meters in front of the lens.

Electrical Resistance Problem:

To find the smaller of the two resistances in a circuit with two resistors in series and two resistors in parallel, we can use the formulas for calculating the total resistance in series and parallel circuits.

Total Resistance in Series: The total resistance \( R_s \) in a series circuit is given by the sum of the individual resistances: \[ R_s = R_1 + R_2 \]

Total Resistance in Parallel: The total resistance \( R_p \) in a parallel circuit is given by the reciprocal of the sum of the reciprocals of the individual resistances: \[ \frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} \]

Let's calculate the total resistance in the given circuit and find the smaller of the two resistances.

Calculation:

Given: - Total resistance of the series circuit \( R_s = 20 \, \Omega \) - Total resistance of the parallel circuit \( R_p = 4.2 \, \Omega \)

Using the formulas for total resistance in series and parallel circuits, we can find the individual resistances \( R_1 \) and \( R_2 \).

From the given total resistance values, we can calculate the individual resistances as follows: \[ R_1 + R_2 = 20 \, \Omega \] \[ \frac{1}{R_1} + \frac{1}{R_2} = \frac{1}{4.2} \]

Solving these equations will give us the values of \( R_1 \) and \( R_2 \).

Comparison of Radii of Curvature:

To compare the radii of curvature of the trajectories of an electron and a proton moving with the same velocity in a uniform magnetic field perpendicular to the lines of induction, we can use the following principles:

1. The force experienced by a charged particle moving in a magnetic field is given by the Lorentz force: \[ \vec{F} = q(\vec{v} \times \vec{B}) \] where: - \( \vec{F} \) = force on the particle - \( q \) = charge of the particle - \( \vec{v} \) = velocity of the particle - \( \vec{B} \) = magnetic field

2.