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alok kumar singh

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2.16 Electric field on one side of a charged body is E1 and electric field on the other side of the same body is E2. If infinite plane charged body has a uniform thickness, then electric field due to one surface of the charged body is given by,

E1? = σ2ε0n? ………….(i)

Where,

n? = unit vector normal to the surface at a point

σ = surface charge density at that point

Electric field due to the other surface of the charged body is given by

E2? = σ2ε0n? ………….(ii)

Electricfieldatanypoint due to the two surfaces,

E2?-E1?=σ2ε0n?+σ2ε0n?=σε0n? ……(iii)

Sinceinsideaclosedconductor,E1?=0,

E? = E2? = σε0n?

Therefore, the electric field just outside the conductor is σε0n?

W

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2.31 (a) Two large conducting spheres carrying charges Q1 and Q2 are brought close to each other. Is the magnitude of electrostatic force between them exactly given by Q1Q2 /4 πε0r2 , where r is the distance between their centres?

(b) If Coulomb's law involved 1/ r3 dependence (instead of 1/ r2 ), would Gauss's law be still true ?

(c) A small test charge is released at rest at a point in an electrostatic field configuration. Will it travel along the field line passing through that point?

(d) What is the work done by the field of a nucleus in a complete circular orbit of the electron? What if t

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alok kumar singh

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2.31 The force between two conducting spheres is not exactly given by the expression Q1Q2 /4 ? ? 0r2 , because there is non-uniform charge distribution on the spheres.

Gauss's law will not be true, if Coulomb's law involved 1r3 dependence, instead of 1r2 , on r

Yes. If a small test charge is released at rest at a point in an electrostatic field configuration, then it will travel along the field lines passing through the point, only if the field lines are straight. This is because the field lines give the direction of acceleration and not the velocity.

Whenever the electron completes an orbit, either circular or elli

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alok kumar singh

Contributor-Level 10

This is a Long Answer type Questions as classified in NCERT Exemplar

Explanation- mass of helicopter m =2000kg

Mass of the crew and passengers m= 500kg

Acceleration a =15m/s2 and g = 10m/s2

a) force on the floor of the helicopter by the crew and passengers

m (g+a)= 500 (10+15)N= 12500N

b) action of rotor of the helicopter on the surroundings air= (m1+m2) (g+a)

= (2000+500) (10+15)= 2500 (25)= 62500N

c) force on the helicopter due to surroundings air

= reaction of force applied by helicopter

= 62500N

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alok kumar singh

Contributor-Level 10

This is a Long Answer type Questions as classified in NCERT Exemplar

Explanation -for the box to just starts sliding down mg

sin θ = t = μ N = μ m g c o s θ

tan θ = μ

θ = t a n - 1 ( μ )

b) when angle of inclination is increased to α > θ

F1= mgsin α - f = m g s i n α - μ N

= mg ( s i n α - μ c o s α )

c) to keep the box stationary, upward force needed F2= m g s i n α +f= mg ( s i n α + μ c o s α )

d) if the box is to move with an upward acceleration a then upward force needed 

F3=mg ( s i n α + μ c o s α )+ma

 

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alok kumar singh

Contributor-Level 10

This is a Long Answer type Questions as classified in NCERT Exemplar

Explanation- on resolving forces into rectangular components in equilibrium forces (F1+1/ 2 )N are equal to 2 N  and F2 is equal to ( 2 + 1 / 2 )N

F1+1/ 2 = 2

F1= 2 - 1 / 2 = 2 - 1 2 = 1 2 = 0.707 N

F2= 2 + 1 2 = 2 + 1 2 = 3 2 = 2.121 N

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alok kumar singh

Contributor-Level 10

This is a Long Answer type Questions as classified in NCERT Exemplar

Explanation – horizontal velocity ux= vs

During projectile motion horizontal velocity remains unchanged

Vx=ux=vs

In vertical direction vy2= uy2+2gH

Vy= 2 g H

Resultant speed of the ball at the bottom

V= v x 2 + v y 2

V= v s 2 + 2 g H

b) when ball is given horizontal velocity and a small downward velocity

in horizontal direction V'x=ux=vs

in vertical direction vy'2= uy2+2gH

resultant velocity of the ball at the bottom

v'= v s 2 + u 2 + 2 g H

 

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alok kumar singh

Contributor-Level 10

This is a Long Answer type Questions as classified in NCERT Exemplar

Explanation- displacement vector of particle is r (t)=? Acos w t + ? Bsinwt

X=Acoswt

x/A= coswt………1

displacement along y axis is

y=Bsinwt

y/B= sinwt……….2

squaring and then adding eqn1 and 2 we get

x2/A2+y2/B2=cos2wt+sin2wt =1

this is an equation of ellipse. Therefore trajectory of particle is an ellipse.

b)v= dr/dt= id/dt (Acoswt)+jd/dt (Bsinwt)

 ? [A (-sinwt)w]+? [B (coswt).w]

= -? Awsinwt+? Bwcoswt

Acceleration a= dv/dt

So a= -? Awd/dt (sinwt)+? Bw [-sinwt]w

=? Aw2coswt-? Bsinwt

= -w2r

So force acting on the particle f=ma=-mrw2

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