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A magnetic field of vecB = 1 xx 10^(-2) hatk tesla applies a force of vec F = (36 hat I + 12 hat j) xx 10^(-23) newton on a proton. Calculate the velocity of proton. |
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Answer» Solution :Let the velocity of PROTON be represented as `vec v = v _(x) hat I + v_(y) hat j + v_(z) hat k` Magnetic FORCE on a charge is given by `vecF = q vec v xx vecB` On substituting the VALUES we get : `vecF = (36 hat I + 12 hat j) xx 10^(-22)` `vecF = (1.6 xx 10^(-19)) (v_(x) hat i+ v_(y) hat j + v_(z) hat k) xx (1 xx 10^(-3) hat k)` ` rArr 36 hat i + 12 hat j = (1.6) (v_(x) hat i + v_(y) hat j + v_(z) hat k) xx ( HATK)` `rArr36/(1.6) hat i + 12/(1.6) hat j = - v_(x) hat j + v_(y) hat i ` ` rArr-v_(x) hat j + v_(y) hat i = 22.5hati + 7.5 hat j` `rArr v_(x) = - 22.5 m//s& v_(y) = 7.5 m//s` `rArrvec v = (-22.5 hati + 7.5 hat j ) m//s` |
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