2. An infinite plate is uniformly charged with charge...

2. An infinite plate is uniformly charged with charge density $\sigma$. Normal vector to the plate is $\hat{i}$. Its velocity is $\mathbf{v}(t) = \theta(t)v_0 \hat{k}$. a. Find magnetic and electrical field as a function of time. b. What is the force (per unit of area) to be applied to the plate to maintain constant velocity? c. What is the energy stored in the fields at instant $t > 0$?

Transcript

00:01 There are two oppositely charged plate.

00:05 The plate a is positively charged and plate b is negatively charged.

00:09 They are held at a distance of 1 .14 centimeter value of d.

00:15 A charge q having a positive charge of 13 .6 microculum is held at a positive plate.

00:26 So at rest, so initial velocity is zero.

00:29 So when charge is released from positive plate, it is attracted towards the negative plate and it reaches a negative plate in the time t equal to 5 .63 microsecond.

00:46 So the mass of the charge is 107 micropoleum.

00:53 So in part a of the problem, we are supposed to find out the acceleration of the charge.

01:07 In part a, we are supposed to find it.

01:10 So we use the equation of motion s equal to ut plus one half a t square for the motion of the charge between the plates a and b.

01:22 So here initial velocity is zero.

01:25 So s is equal to one half a t square.

01:31 This gives a is equal to 2s upon t square.

01:40 S is the distance between the plates, right? and t is the time taken by charge to travel between the plates.

01:50 So this is the value of s.

01:55 Sometime we call it d also.

01:59 So this is s, right? and t is the time 5 .63 microsecond.

02:08 So we put these values 2 into s is 0 .0114 meter divided by 5 .63 into 10 x to minus 6 whole square, it comes out to be 7 .19 into 10 to 8 meter per second square which is equal to 7 .19 into 10 x to 11 millimeter per second square.

02:50 This is the answer for the first problem.

03:00 In the second problem, we are supposed to find out the electric field.

03:10 Now the electric field, we know the force acting on the charge is equal to the value of charge multiplied by the electric field.

03:21 And from newton's second law, we also know that force is equal to mass into acceleration.

03:27 If we equate equation 1 and 2, then we get qe is equal to ma.

03:40 It means e equal to ma upon q...

Question

Please give Ace some feedback