A long conducting circular rod is inside a long conducting square enclosure. htt

Question

A long conducting circular rod is inside a long conducting square enclosure.

http://i.imgur.com/Aa0B61P.png

The rod is maintained at a potential of -5000 volts with respect to the square which is grounded (V=0). The contour lines are equipotentials with V = -4000, -3000, -2000, and -1000 volts.

http://i.imgur.com/ux9rWpf.png

PART A

Select a response for each statement below. (Use 'N', North, towards top of page (+y dir), and 'E', East, to the right (+x dir), 'NE' for in between 'N' and 'E', etc.) OR True/False

1) The magnitude of the E-field at 5 is greater than that at 7 .

2) The y-component of the E-field at 5 is zero.

3) The direction of the force on a small (+) charge at 5 is ....

4) The direction of the force on a small (-) charge at 9 is ....

5) The magnitude of the E-field at 6 is very small (~ zero).

6) The direction of the E-field at 3 is ....

7) The x-component of the E-field at 7 is positive.

Explanation / Answer

Equipotential lines (projections of equipotential surfaces) are close to each other where magnitude of the electric field is larger and equipotential lines are less close to each other where magnitude of the electric field is lesser.

From figure equipotential surfaces are getting further from each other as we go towards the square.

1) Hence magnitude of E field at 5 is greater than the magnitude of E field at 7.

TRUE

_____________________

At any point on an equipotential surface electric field is normal to the surface. Also the direction of electric field is from higher potential to lower potential.

2) Electric field at point 5 is towards (-x direction) or west , W. Hence Y component of E field at point 5 is zero.

TRUE

3) The direction of force on a positive charge at a point is same as direction of electric field at the point. Electric field at point 5 is towards (-x direction) or west , W.

4) The direction of force on a negative charge at a point is opposite to the direction of electric field at the point. Electric field at point 9 is towards (-y direction) or South Hence force on a negative charge at point 9 is towards North, N.

5) Refer to the points mentioned above 1). Since equipotential surfaces are farthest at point 6, magnitude of the E-field at point 6 is very small (~ zero). TRUE.

6)

Direction of electric field at point 3 is along NorthEast, NE.

7)

Direction of electric field at point 7 is along SouthEast. Hence x-component of electric field at point 7 is poistive,

TRUE.

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