The figure shows a cross-section of a large metal sheet carrying an electric current along its surface. The current in a strip of width dl is Kdl where K is a constant. The magnetic field at a point P at a distance x from the metal sheet will be:
The figure shows a cross-section of a large metal sheet carrying an electric current along its surface. The current in a strip of width dl is Kdl where K is a constant. The magnetic field at a point P at a distance x from the metal sheet will be:
The correct option is C Doesn’t depend on x
Consider two strips A and C of the sheet situated symmetrically on the two sides of P (figure 35-W11a). The magnetic field at P due to the strip A is Ba perpendicular to AP and that due to the strip C is Bc perpendicular to CP. The resultant of these two is parallel to the width AC of the sheet. The field due to the whole sheet will also be in this direction. Suppose this field has magnitude B.
The field on the opposite side of the sheet at the same distance will also be B but in opposite direction. Applying Ampere’s law to the rectangle shown in figure (35-W11b),
2Bl=μ0KlOr, B=12μ0K
Note that it is independent of x.
Doesn’t depend on x
Consider two strips A and C of the sheet situated symmetrically on the two sides of P (figure 35-W11a). The magnetic field at P due to the strip A is Ba perpendicular to AP and that due to the strip C is Bc perpendicular to CP. The resultant of these two is parallel to the width AC of the sheet. The field due to the whole sheet will also be in this direction. Suppose this field has magnitude B.
The field on the opposite side of the sheet at the same distance will also be B but in opposite direction. Applying Ampere’s law to the rectangle shown in figure (35-W11b),
2Bl=μ0KlOr, B=12μ0K
Note that it is independent of x.
