Home
Class 12
PHYSICS
At a distance r from a point located at ...

At a distance r from a point located at origin in space, the electric potential varies as `V= 10r`. Find the electric field at `vecr = 3hati + 4 hatj - 5hatk`.

A

`(sqrt2)(3hati+4hatj-5hatk)`

B

`(-sqrt2)(3hati+4hatj-5hatk)`

C

`(-sqrt3)(3hati+4hatj-5hatk)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`V=10r=10sqrt(x^(2)+y^(2)+z^(2))`
`E_(x)=-(dv)/(dx)=-(10(2x))/(2sqrt(x^(2)+y^(2)+z^(2)))`
`=(-10x)/(sqrt(x^(2)+y^(2)+z^(2)))=(10xx3)/(sqrt(3^(2)+4^(2)+5^(2)))=-3sqrt(2)`
similarly
`E_(y)=-4sqrt(2)`
`E_(x)=5sqrt(2),ver(E)=E_(x)hat(i)+E_(y)hat(j)+E_(z)hat(k)`
Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS VOLUME 3

    CENGAGE PHYSICS|Exercise Multiple Correct Answer type|109 Videos

  • MISCELLANEOUS VOLUME 3

    CENGAGE PHYSICS|Exercise Assertion and Reason Type|8 Videos

  • MECHANICAL PROPERTIES OF SOLIDS

    CENGAGE PHYSICS|Exercise Question Bank|4 Videos

  • MISCELLANEOUS VOLUME 5

    CENGAGE PHYSICS|Exercise Integer|12 Videos

Similar Questions

Explore conceptually related problems

The potential at a point in an electric field is give by V=Rr volt where r is distance of the point from the origin of the co-ordinate system. Find the electric field at a point r=(hati+2hatj+2sqrt(5)hatk)m

Let V_0 be the potential at the origin in an electric field vecE = 4hati + 5hatj . The potential at the point (x,y) is

Electric potential at any point V=-4x+3y+5z then magnitude of electric field in the space will be

The variation of potential with distance R from the fixed point is shown in (Fig. 3.125). . The electric field at R = 5 m is.

The variation of potential with distance R from a fixed point is shown in figure. The electric field at R = 5 m is -

The variation of potential with distance r from a fixed point is shown in fig. The electric field at r = 5cm, is :

Find the distance of the point with position vector - hati - 5 hatj - 10 hatk from the point of intersection of the line vec(r) = (2 hati - hatj + 2 hatk) + lambda ( 3 hati + 4 hatj + 12 hatk) with the plane vec(r). (hati - hatj + hatk) = 5 .

The electric field and the potential of an electric dipole vary with distance r as

A positive charge 50 muC is located in xy plane at a position vector r_0 = 4hati + 4hatj . the electric field strength E at a point whose position vector is vecr = 10hati - 4hatj is ( vecr_0 and vecr are expressed in metre)