If the frequency of the voltage signal impressed on the parallel plate capacitor is doubled from f to 2f, the amplitude of the magnetic field bo at r = a at the mid-plane of the gap between the plates of this capacitor will: increase by a factor of two. remain the same. decrease by a factor of four. decrease by a factor of two. increase by a factor of four.

Increase by a factor of four

Explanation:

Given data

capacitor =  f to 2f

r = a

to find out

capacitor will be

solution

first we calculate the current

displacement current will be = ɛ × electric flux  

displacement current will be  = ɛ × electric flux

electric flex = A × electric field

electric field = voltage / d

electric field = V(o) sin ωt / d

so electric flex

electric flex = A ×  V(o) sin ωt / d

and displacement current will be

displacement current = ɛ × A ×  V(o) sin ωt / d

so the magnetic filed will be here

magnetic filed = μ × current + μ × ɛ d∅/dt

so we can say that frequency will be double when magnetic field increase

so Increase by a factor of four

the velocity you are looking for is made up of two parts: horizontally velocity, vh, and its vertical velocity, vv. the actual velocity of the ball will be these two parts added together, and because velocity is a vector then they will need to be added vectorially.  

neglecting air resistance etc etc.,  

the horizontal velocity component will be constant (because there is no accelerating force in the horizontal direction.  

vh = 8 ms-1  

the vertical velocity component has an accelerating force: 'g'.  

using v = u +at where a = g = 9.81 ms-2.  

the vertical component of velocity, vv = 0 + gt = vv =9.81 x 2  

vv = 19.62 ms-1 . the zero appears because the virtical component of velocity at time t=0 is zero. remember, the ball was thrown horizontally.  

how fast it will be moving (it actual path (being a parabola )) will be the vector sum of these two.  

adding vectorally gives: -  

v = sqr root (8^2 + 19.62^2) = sqr root(64+384.9) = 21.18 or 21.2 ms-1

spectral lines lyman is one set