Electric charges and fields: Crossed dipoles

[Ujjwal28]

Homework Statement

Two short dipoles each of dipole moment p are placed art origin. The dipole moment of one dipole is along x-axis while that of other is along y axis. Then what will be the electric field at a point (a, 0)?

Homework Equations

The direction of electric field due to axial dipole has to be along +ve x-axis while electric field due to equatorial dipole should be towards -ve x axis.

The Attempt at a Solution

So shouldn't the net electric field at (a, 0) be
E=2kp/a³-kp/a³
Well the answer is k5^0.5p/a³.can someone please explain where I am wrong?

 

[rl.bhat]

Check the direction of the electric field due to a dipole along the equatorial direction.

 

[Ujjwal28]

Ok isn't the direction of electric field at equatorial line anti parallel to that of direction of electric filed at axial line?
Where am I wrong?

 

[rl.bhat]

Ok isn't the direction of electric field at equatorial line anti parallel to that of direction of electric filed at axial line?
Where am I wrong?

Yes. Check it again.

 

[Ujjwal28]

Ok so is it perpendicular to the direction of electric field on axial line?

 

[rl.bhat]

Yes. Along -y axis. Now calculate net electric field at ( a,0)

 

[Ujjwal28]

Ok do I the electric field due to axial line is taken to be from left to right i.e along +ve x-axis , will the electric field due to axial line be perpendicular towards +ve y axis? And then adding the two fields vectorially I get the answer?

 

[rl.bhat]

Ok do I the electric field due to axial line is taken to be from left to right i.e along +ve x-axis , will the electric field due to axial line be perpendicular towards +ve y axis? And then adding the two fields vectorially I get the answer?

Check this statement

 

[Ujjwal28]

Sorry can you explain?

 

[rl.bhat]

Sorry can you explain?

For the dipole along y-axis, the point ( a,0 ) lies on the equatorial line and the electric field is along - y axis.