Electric Charges And Fields

In vector form, we write expressions of field at

A%2C%20B

and

C

E%20_%7BA%7D%20%3D%5Cleft%5C%7B%5Cfrac%7Bk%20q%7D%7B%5Cleft(1%5E%7B2%7D%2B2%5E%7B2%7D%2B3%5E%7B2%7D%5Cright)%5E%7B3%20%2F%202%7D%7D%5Cright%5C%7D(%5Chat%7B%20i%20%7D%2B2%20%5Chat%7B%20j%20%7D%2B3%20%5Chat%7B%20k%20%7D)

E%20_%7BB%7D%20%3D%5Cfrac%7Bk%20q%7D%7B%5Cleft(1%5E%7B2%7D%2B1%5E%7B2%7D%2B(-1)%5E%7B2%7D%5Cright)%5E%7B3%20%2F%202%7D%7D%20%5Ccdot(%5Chat%7B%20i%20%7D%2B%5Chat%7B%20j%20%7D-%5Chat%7B%20k%20%7D)

E%20_%7BC%7D%20%3D%5Cfrac%7Bk%20q%7D%7B%5Cleft(2%5E%7B2%7D%2B2%5E%7B2%7D%2B2%5E%7B2%7D%5Cright)%5E%7B3%20%2F%202%7D%7D%20%5Ccdot(2%20%5Chat%7B%20i%20%7D%2B2%20%5Chat%7B%20j%20%7D%2B2%20%5Chat%7B%20k%20%7D)

So,

E%20_%7BA%7D%20%3D%5Cfrac%7Bk%20q%7D%7B14%5E%7B3%20%2F%202%7D%7D(%5Chat%7B%20i%20%7D%2B2%20%5Chat%7B%20j%20%7D%2B3%20%5Chat%7B%20k%20%7D)

E%20_%7BB%7D%20%3D%5Cfrac%7Bk%20q%7D%7B3%5E%7B3%20%2F%202%7D%7D(%5Chat%7B%20i%20%7D%2B%5Chat%7B%20j%20%7D-%5Chat%7B%20k%20%7D)

E%20_%7BC%7D%20%3D%5Cfrac%7Bk%20q%7D%7B12%5E%7B3%20%2F%202%7D%7D(2%20%5Chat%7B%20i%20%7D%2B2%20%5Chat%7B%20j%20%7D%2B2%20%5Chat%7B%20k%20%7D)

As,

E%20_%7BA%7D%20%5Cperp%20E%20_%7BB%7D%3D0

and

E%20_%7BB%7D%3D4%5Cleft%7C%20E%20_%7BC%7D%5Cright%7C

Chapter Questions
1 MCQs