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A clock face has negative charges -q, -2q, -3q,.....-12q fixed at the position of the corresponding numerals on the dial. The clocj hands do not disturb the net field due to the point charges. At what time does the hour hand point in the direction of the electric field at the centre of the dial? |
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Answer» Solution :Let distance of each charge from unit charge at centre 'O' = r. Resultant ELECTRIC field of each charge, `E=1/(4pi epsi_(0)) (6q)/r^(2) [ :' -6q-(-12 q)]` Let OX be the reference AXIS, The angles of resultant fields with OX-axis shown.  Resultant field along OX-axis `=(0+1/2+sqrt(3)/2+1+sqrt(3)/2+1/2)i=(2+sqrt(3))i` Resultant field along OY-axis `=(1+sqrt(3)/2+1/2+0-1/2-sqrt(3)/2) hat(j)=1 hat(i)` `:.` Resultant electric field, `E_(R_((OH)))=(2+sqrt(3)) hat(i)+1 hat(j)` The DIRECTION of resultant field (OH) is given by, `tan theta=(|OY|)/(|OX|)` `=tan theta=1/(2+sqrt(3))=tan 15^(@)` `implies theta=15^(@)`, with OX-axis. `:.` The hour hand SHOWS at the centre of the dial is at 9.30. |
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