Home
Class 12
PHYSICS
An infinite sheet carrying a uniform sur...

An infinite sheet carrying a uniform surface charge density `sigma` lies on the xy-plane. The work done to carry a charge q from point `vec(A) = a(hat(i)+2hat(j)+3hat(k))` to the point `vec(B) = a(hat(i)-2hat(j)+6hat(k))` (where a is a constant with the dimension of length and `epsilon_(0)` is the permittivity of free space) is

A

`(3 sigma aq)/(2epsilon_(0))`

B

`(2 sigma aq)/(epsilon_(0))`

C

`(5 sigma aq)/(2epsilon_(0))`

D

`(3 sigma aq)/(epsilon_(0))`

Text Solution

Verified by Experts

The correct Answer is:
A
Distance between the points , `vec(r ) = vec(B) - vec(A) = a(-4hat(j)+3hat(k))`
Field intensity sheet carrying a uniform surface charge density `sigma` lies on the xy-plane,
`vec(E ) = (sigma)/(2epsilon_0)hat(k)`
`:.` Electric force acting on the charge `q , vec(f) = qvec(E ) = (qsigma)/(2 epsilon_0)hat(k)`
`:.` Work done, `W = vec(F) cdot vec(r) = (q sigma)/(2epsilon_0) hat(k) a(-4hat(j)+3hat(k))=(3q sigma a)/(2epsilon_0)`.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • ELECTRIC POTENTIAL

    CHHAYA PUBLICATION|Exercise Examination Archive with solutions (JEE Main)|3 Videos

  • ELECTRIC POTENTIAL

    CHHAYA PUBLICATION|Exercise Examination Archive with solutions (AIPMT)|2 Videos

  • ELECTRIC POTENTIAL

    CHHAYA PUBLICATION|Exercise Examination Archive with solutions (WBCHSE)|8 Videos

  • ELECTRIC FIELD

    CHHAYA PUBLICATION|Exercise CBSE SCANNER|31 Videos

  • ELECTROMAGNETIC INDUCTION & ALTERNATING CURRENT

    CHHAYA PUBLICATION|Exercise CBSE SCANNER|28 Videos

Similar Questions

Explore conceptually related problems

If the projection of vec(a) = lamda hat(i) + hat(j) + 4hat(k) " on " vec(b) = 2hat(i) + 6hat(j) + 3hat(k) is 4 units, then find lamda

Find the area of triangle (i) drawn on the vectors vec(a) = 6 hat (i) + 2 hat (j) - 3 hat (k) and vec (b) = 4 hat (i) - hat (j) - 2 hat (k)

Knowledge Check

  • The lines vec(r)=hat(i)+t(5hat(i)+2hat(j)+hat(k)) and vec(r)=hat(i)+s(-10hat(i)-4hat(j)-2hat(k)) are -

    A
    parallel
    B
    skew
    C
    coincident
    D
    none of these

  • The scalar projection of vec(a) = 2 hat (i) - 3hat(j) + hat (k) on vec (b) = 3 hat(i) - 6 hat (j) - 2 hat (k)

    A
    `22/7`
    B
    `26/7`
    C
    `22/(sqrt(14))`
    D
    `26/(sqrt(14))`

  • If vec (a) = 2 hat (i) - 3 hat (j) + 4 hat (k) and vec(b) = - 6 hat (i) + 9 hat (j) - 12 hat (k) , then

    A
    `vec(a) bot vec(b)`
    B
    `vec(a) "||"vec(b)`
    C
    angle between the vectors is `cos^(-1). 3/4`
    D
    angle between the vectors is `pi/3`

    • Similar Questions

    Explore conceptually related problems

    If vec(a)=2hat(i)-5hat(j)+3hat(k) " and " vec(b)=hat(i)-2hat(j)-4hat(k) , find the value of abs(3vec(a)+2vec(b)).

    Find lambda where projection of vec (a) = lambda hat (i) + hat (j) + 4 hat (k) on vec (b) = 2 hat (i) + 6 hat (i) + 3 hat (k) is 4 unit

    Find a unit vector perpendicular to both the vector vec(a) = 2 hat(i) + hat(j) - 2 hat(k) and vec(b) = 3 hat (i) - hat (j) + hat (k)

    The value of lamda for which the vectors vec(a) = hat(i) + 3hat(j) - hat(k) and hat(b) = 2hat(i) + 6hat(j) + lamda hat(k) are parallel is-

    If vec (a)= 2 hat (i) - hat (j) + hat (k) and vec(b) = - hat (i) + 3 hat (j) + 4 hat (k) , then value of vec (a). vec(b) is -

    Home
    Profile